Math Quiz | Only Genius Can Solve This ?

Added: 2026-05-05

[00:01:29]All right, guys. So, this is the very first question.

[00:01:34]And we need to solve for the value of U here.

[00:01:39]So, just take your time, think about it, and let's see how many of you can do this.

[00:01:44]This is just a warm-up question. Cano is already here. Hi, Cano. Thanks for joining.

[00:01:49]Hi, Hirain.

[00:01:53]Siddharth is also here. Siddharth is saying 20. That's so quick, guys.

[00:01:58]Hi, Siddharth. Thanks for joining.

[00:02:01]So, let's just wait for a few more participants.

[00:02:08]And then I'll just close the answer for this, and we'll move to the next also.

[00:02:20]Anyone else, guys, who is good who want to give the answer for this?

[00:02:26]Hirain is also saying 20. So, three users has given the answer. Let's see if it is 20 or not.

[00:02:31]First of all, if I will talk about this triangle only, this is an equilateral triangle, right? So, all of these angles are definitely going to be 60°.

[00:02:41]So, if I will mark the corner angles of this triangle, this is going to be 60, so this angle is 60. Similarly, corner angle of square is 90°, we know that.

[00:02:51]So, we have this like already, this is 10, this is 60, and this is 90. So, 90 + 60 is 150 + 10 160 + U is going to be equal to 180. So, therefore, U is going to be 20°. So, that's the correct answer.

[00:03:06]We'll move to the next, and let's see how many of you can answer that.

[00:03:11]Let's have this, guys.

[00:03:14]Be quick with this one, guys.

[00:03:16]We need to solve for the value of X + Y.

[00:03:19]The second question.

[00:03:24]Take your time.

[00:03:25]Let's see how many of you can answer this.

[00:03:35]We need to solve for the value of X + Y.

[00:03:40]Black Avenger is here.

[00:03:59]Anyone with the answer for this one, guys?

[00:04:05]Hirain is saying 40.

[00:04:08]Okay. So, what is your explanation for that, Hirain?

[00:04:11]Guys, don't just throw your answers for this because we are not having rapid fire right now. We do need the explanation along with the correct answers.

[00:04:21]So, a brief a brief explanation is required.

[00:04:49]Anyone else, guys?

[00:04:53]Who can give the answer along with the correct approach?

[00:05:09]Dark Wing is here who's saying 45.

[00:05:17]And Black Avenger is also saying the same.

[00:05:21]Black Avenger has given his answer along with the explanation. We'll check it.

[00:05:27]We'll check whether it is 45 or not.

[00:05:29]Let's see.

[00:05:35]Okay.

[00:05:38]Subway Rushing Gaming is also saying 45.

[00:05:40]Cano is saying 45. Cano has given the explanation also. Let's see, guys, if it is 45 or not.

[00:05:45]First of all, if I will talk about this triangle, this is an isosceles triangle, so its base angle must be equal, right? I can use the angle sum property and solve for the base angle.

[00:05:55]This is going to be 66 each.

[00:05:58]Similarly, these triangle this All of these sides are marked equal, which means this triangle is an equilateral triangle, so every single angle is going to be 60°.

[00:06:07]Now, using the linear pair property, we can say straight angle property, we can add all of these three angles together and solve for the value of Y and equate it to the 180°, right? So, 3Y + 66 + 60 is equal to 180°, and from here, I'll be getting Y Y as 18.

[00:06:25]So, now, Y If Y is 18, so I can say 3Y we here 2X is equal to 3Y. Therefore, 3Y is going to be 18 * 3, which is going to be 54.

[00:06:38]And X is going to be 27. So, we have X as 27, Y as 18. Adding both X and Y together will give you 27 + 18, so your answer is going to be 45.

[00:06:50]45 is the right answer, guys. We'll move to the next.

[00:06:54]Let's have the next one, guys.

[00:06:57]Give me a minute, guys.

[00:07:02]Just give me a minute.

[00:07:11]Okay.

[00:07:13]Let's have this.

[00:07:16]We need to solve for the shaded region area.

[00:07:21]I hope it is visible.

[00:07:25]Yep. It's visible.

[00:07:30]Solve for the shaded area.

[00:07:32]Give your answer along with the correct approach. Let's see how many of you can answer this.

[00:07:52]Math is fun is here. He's saying 10.

[00:07:55]Dark Wing is saying 10.

[00:08:04]Ice is here who's saying 10.

[00:08:08]Okay.

[00:08:10]Cano is saying same, 10 10 10. So, I can see most of the users are giving answer as 10.

[00:08:16]We'll see if it is 10 or not.

[00:08:22]Let's have a look.

[00:08:29]See, guys.

[00:08:30]If I'm going to take this this is one unit, and this is going to be three.

[00:08:39]I can solve for this. This is nothing but the side using the This is a hypotenuse of this triangle, but I can solve for this, and this would be a side of the square.

[00:08:47]So, side of the square is going to be 3 squared plus 1 squared root, like side is going to be root of 3 squared, which is 9, plus 1 squared, which is 1, so it's going to be root 10.

[00:08:58]So, if root 10 is the side, therefore, area is going to be side squared, so side squared is going to be 10 only. So, the area of the square, or we can say the shaded region area is 10 units.

[00:09:10]So, 10 is the right answer, guys. We'll move to the next.

[00:09:13]Let's have the next one.

[00:09:16]Let's see how many of you can do this.

[00:09:18]Be quick with this one, guys.

[00:09:36]Guys, we need to solve for the value of X.

[00:09:44]Be quick with this one, guys.

[00:10:01]>> We have to solve for the value of x.

[00:10:06]Take your time, think about it.

[00:10:21]Diya Pari saying nine.

[00:10:24]Nine maybe she's answering for the previous question.

[00:10:28]Math is fun saying 16.

[00:10:31]Dark Fang is saying 120.

[00:10:37]Dark Fang now corrected himself to 60.

[00:10:40]Okay.

[00:10:42]Kanu is saying 60.

[00:10:46]Okay, so I can see three users. Sheila is also here. Sheila is saying 60. Black Avenger 60.

[00:10:52]All right, so everyone is giving answer 60 for this. We'll see if it is 60 or not.

[00:11:00]Let's see.

[00:11:04]Siddharth is also saying it is 60. Okay, guys, let's check if it is 60 or not.

[00:11:08]Let's see.

[00:11:10]First of all, this is 60 and 60. These two angles are 60, so definitely this angle is going to be an exterior angle to this triangle.

[00:11:20]This is going to be 120.

[00:11:22]Now this is 60, this is 60, this is 120, this is also going to be 120 because this is making an isosceles trapezoid.

[00:11:29]And we know the base angle of isosceles trapezoid are equal. Subway Rush gaming 60 is the right answer. You guys were correct.

[00:11:37]Let's see. Just give me a minute, guys.

[00:11:41]My pen is not working right now.

[00:11:45]Just a minute.

[00:12:52]Guys, just give me a minute.

[00:14:12]Guys, just give me a minute, guys. It's lagging.

[00:14:16]Something is happening here.

[00:14:19]There is an issue.

[00:14:33]Okay, I hope it is fine now.

[00:14:38]Yep.

[00:14:39]So I was saying like we have solved for this these two angles are already 60.

[00:14:43]This angle is going to be an exterior angle to this. This was 120.

[00:14:47]And as we can see this is nothing but an isosceles trapezoid. This is also going to be one 20 because base angle of isosceles trapezoid are equal.

[00:14:57]So now you can solve for the value of x is easily.

[00:15:00]Right? So 120 + x is equal to 180.

[00:15:03]Therefore, x is going to be 60°.

[00:15:06]So you guys were correct already. You have given the answer as 60°.

[00:15:10]We'll move to the next.

[00:15:12]Let's see how many of you can answer this, guys.

[00:15:15]Uh let's have the next one.

[00:15:22]We need to solve for the area. Area of the semi-circle here. Be quick, guys.

[00:15:26]You are going to give your answer in terms of pi only.

[00:15:35]Give your answer in terms of pi.

[00:15:44]Good evening, Will.

[00:15:49]49 pi 24 49 by 2 pi Sheila 24.5 pi. Okay.

[00:15:57]49 by 2 pi 24.5 All right.

[00:16:03]So this is easy.

[00:16:06]Abhishek is also saying the same 49 pi by 2.

[00:16:09]This is square, right? We can solve for the side of the square. Area is already given. The side is going to be 7 into 7, so this is 7.

[00:16:17]Now this 7 is a side of the square, but it is also the radius of the semi-circle, right? So we have the radius of the semi-circle. Therefore, we can solve for the area.

[00:16:25]Area is going to be pi r squared by 2, so it's pi 7 squared by 2. It's going to be 49 pi by 2.

[00:16:33]So 49 pi by 2 is correct answer. You guys were correct.

[00:16:37]We'll move to the next and let's see how many of you can answer this, guys.

[00:16:43]Again, we need to solve for the value of x. This is easy.

[00:16:50]Be quick with this one, guys.

[00:16:52]We need to solve for the value of x.

[00:16:59]Take your time.

[00:17:01]Himanshu is saying 70. We are solving for x, Himanshu.

[00:17:07]290. Okay.

[00:17:09]Sheila is also saying the same 290.

[00:17:17]Dark Fang is saying 310.

[00:17:21]Will is saying 290. Okay.

[00:17:24]We'll see if it is 290.

[00:17:27]Hiren is saying 290. Just Guy is also saying 290. All right, so most of you has already given the answer as 290.

[00:17:34]Let's see if it is 290 or not.

[00:17:37]So this is 95, this is 105. 95 + 105 is going to be 200. Plus this 90 is 290, right?

[00:17:45]So we can solve for this missing angle.

[00:17:48]Right? That missing angle of the quadrilateral using the angle sum property of the quadrilateral, it's going to be 70.

[00:17:55]And x + 70 is going to make a complete angle, guys.

[00:17:58]Right?

[00:18:00]So therefore, the answer for x is going to be 290.

[00:18:07]This is going to be 70°, so x + 70 is equal to 360 and therefore, x is going to be 290. So 290 is the correct answer, guys. 310 is not the right answer.

[00:18:19]We'll move to the next.

[00:18:21]All right.

[00:18:24]Let's have this, guys.

[00:18:28]Solve for the value of x.

[00:18:30]Let's see who is going to give the answer first.

[00:18:39]Let's just solve for the value of x.

[00:19:04]Hiren, are you talking about this puzzle like the question on the screen?

[00:19:10]>> [snorts] >> Just Guy saying 150. Dark Fang is saying 150. Black Avenger saying 150.

[00:19:17]Okay.

[00:19:18]Abhishek is saying 120.

[00:19:23]No, all. They are not from any of the book.

[00:19:26]Few of them are from some of the books that I already have. I prefer so many of the geometry books.

[00:19:38]Shubham saying Math is fun 150. Sheila is saying 150.

[00:19:42]Great.

[00:19:44]So 150 is the correct. They are saying all of them are saying 150. Let's see if it is 150 or not. I'll give the explanation for that.

[00:19:51]Let's have a look.

[00:19:55]Okay. So, first of all uh we can see there are multiple approaches, guys. First of all, if I'll this is 150, I can solve for this angle, this would be 30 using the linear pair.

[00:20:07]And as this triangle is an isosceles triangle, so the base angle for this triangle must be equal. So, this is also going to be 30.

[00:20:14]Right?

[00:20:15]So, 30 30, we do have 30 and 30. I can solve for this angle using the angle sum property, this is going to be 120.

[00:20:23]And if I look on this angle this much is going to be equal to this 30. Why?

[00:20:27]Because they are alternate interior angle. These lines are parallel, so this is 30.

[00:20:32]Now, see this angle X and this entire angle X, they are they are equal. Like X is going to be 120 + 30, it's going to be 150. So, 150 is the right answer.

[00:20:44]Yes, Will, you are also correct.

[00:20:46]So, we'll move to the next.

[00:20:48]Let's have a good one.

[00:20:50]Let's see how many of you can do this, guys.

[00:20:55]We need to solve for the area of the circle.

[00:20:58]The given figure is a square, it is given to us. We need to solve for the area of the circle.

[00:21:11]I hope it is visible, guys.

[00:21:14]Yeah.

[00:21:16]It's there now.

[00:21:22]Solve for the area of the circle.

[00:21:36]Irene is also a teacher, okay.

[00:21:38]That's nice, hey.

[00:21:49]Guys, take your time, think about it, and give your answer along with the correct approach.

[00:21:55]Let's see how many of you can answer this.

[00:21:59]And you are going to give your answer in terms of pi only. Don't give your answer in decimals.

[00:22:20]You can think, Will.

[00:22:22]Take your time.

[00:22:32]Guys, don't just throw your answers. I already told you.

[00:22:36]Give your answer along with the correct approach. We are solving for the area of the circle.

[00:23:13]Great. Random has given his explanation.

[00:23:16]We'll see if it is correct or not later.

[00:23:18]Let's just wait for a few more participants to give the answer, guys.

[00:23:47]Yes, I know. I'll Just give me a minute, guys.

[00:23:59]I hope it is visible again.

[00:24:01]Phoenix is saying 9 pi.

[00:24:03]Math is fun saying three.

[00:24:06]Dark Fang has given the equation also, okay.

[00:24:14]All right, guys. We'll see if it is like we do have so many of users already saying 9 pi as answer.

[00:24:21]But only Random and Dark Fang, they have given the explanation.

[00:24:25]Math is fun also saying the same.

[00:24:31]Okay.

[00:24:36]Let's see if it is correct or not. Let's see 3 pi is correct or not.

[00:24:40]See, this is eight, right? The eight is the radius of this quadrant. Like both because both of the quadrants are having the same radius.

[00:24:48]If I'm going to mark the center of the quadrant, if I'm going to draw a line This is the point of tangency passing through this point of tangency, right?

[00:24:57]So, we can see this is this entire length is eight.

[00:25:01]This is also going to be the radius of the quadrant, right?

[00:25:04]This is radius of the quadrant only.

[00:25:07]Now, this is eight. This much length is R.

[00:25:11]This much length is R.

[00:25:13]We are left with this length, and this is going to be 8 minus R.

[00:25:17]Correct?

[00:25:18]This length is going to be 8 minus R.

[00:25:20]I'll erase this. This is 8 minus R.

[00:25:25]Now, talk about this one. This is going to be R only.

[00:25:29]And as this is perpendicular to this chord or whatever we say, like it's a tangent to the circle, but it is perpendicular, so definitely it is going to bisect eight. So, this would be four each, four four.

[00:25:41]We can take the triangle. This is a triangle we have, so we can apply the Pythagorean theorem here.

[00:25:47]8 minus R squared is equal to R squared plus four squared.

[00:25:51]And if I'm going to solve this I'm explaining.

[00:25:56]I hope it is visible, Irene.

[00:25:59]So, if I'm going to solve this further, I'll be getting an equation and using solving that equation Let me just write the equation also. 64 16 R plus R squared is equal to R squared plus 16. R squared R squared will get cancelled out.

[00:26:13]And I'll be having 64 minus 16 R is equal to 16.

[00:26:18]And if I'm going to solve this further I'll be getting minus 16 R is equal to minus 48. Therefore, R is equal to three.

[00:26:26]So, once we have the value of R, that's what we need to solve. We have the R, we can solve for the area. Area is going to be pi R squared. It's pi three squared.

[00:26:35]So, 9 pi is the right answer, guys.

[00:26:38]Shubham, Black Avenger, Sheila, you guys were correct. I hope it is clear to every one of you guys.

[00:26:44]Anyone having any doubt in this one?

[00:26:47]They can ask.

[00:26:48]Or else we can move to the next.

[00:26:58]Welcome, Shubham.

[00:27:01]All right, guys. We'll have the next one.

[00:27:04]Just give me a minute.

[00:27:07]I need to select a good question for you. Let's have this.

[00:27:13]Okay, Random dude is saying, "Please explain again."

[00:27:18]Wait a sec. I'll Okay. Here we were.

[00:27:22]See.

[00:27:25]I am not going to ex- give the ex- entire explanation. I'll give you the triangle, like This was eight, I told you, because this is nothing but the radius. This is radius, this is eight.

[00:27:36]So This is the quadrant radius. Side of the square is nothing but the radius of the quadrant. So, this length is going to be eight, right? Entire length.

[00:27:44]Now, see if I talk about this much portion, this is R, radius of the circle. We are left with this length.

[00:27:49]This is This much length is going to be 8 minus R.

[00:27:55]And this is also the radius of the circle. So, it's going to be R. And as it is a point of contact to the circle, so it's going to be a perpendicular.

[00:28:03]Like radius are perpendicular to the tangent, we know that. And it is definitely going to bisect this side.

[00:28:08]Right? So, this is eight. Like this length is also eight.

[00:28:12]So, this would be four each.

[00:28:14]Right? Now, take this triangle. We have all of the side of the triangle, and using the Pythagorean theorem, you will get the value of R. If you are going to frame a theorem like equation for this R is going to be three.

[00:28:28]So, if R is going to be three, you can solve for the area easily. I hope it is clear.

[00:28:35]Shall we move to the next? Just guy dude, I hope it is clear to you.

[00:28:44]Siddharth saying, "Yes."

[00:28:47]I hope it is clear, so we'll move to the next, guys.

[00:28:53]Let's have the next one, guys.

[00:28:57]We have this. We need to solve for the shaded region area again. Multiple approaches are possible for this question, guys.

[00:29:04]So, just give your answer along with the correct approach.

[00:29:17]We need to solve for the shaded region area.

[00:29:23]The red dot that you can see, guys, that is the center of the bigger circle.

[00:29:29]And the for the smaller circle, it is already given to you. You can see that.

[00:29:34]Let's see who is going to give your ans- give the answer first.

[00:29:37]And you are going to give your answers in terms of pi.

[00:29:42]Think about it.

[00:29:44]Take your time.

[00:30:06]>> Again, explanation is still missing, guys.

[00:31:00]The points marked form a triangle.

[00:31:03]Side R and R 4 and R - 2 this follows R is equal to R + 4.

[00:31:11]56 pi you guys were saying.

[00:31:14]Pythagoras Okay. So, you guys have used Pythagorean theorem. All right.

[00:31:21]There is another approach.

[00:31:25]So, let's see if anyone of you can answer using that approach. We'll wait for few more minutes to give a few more participants to give the answer and then we'll move to the next.

[00:32:02]All right, Black Avenger is here R - 6.

[00:32:14]Great.

[00:32:18]All right, guys. So, I can see that most of you has given the answer as 56 pi already.

[00:32:27]Let's see. I'm not going to use the Pythagorean theorem. You guys can use the Pythagorean theorem. I'm assuming the radius of the bigger circle as capital R and radius of the small circle is already given to you as small r, right?

[00:32:40]So, let's just use the intersecting chord theorem. We do have intersecting chord theorem, guys. We can use for this. Like I can have this I can have the These are going to be equal for sure. If R is the radius of the bigger circle, then this much length is going to be R - 6.

[00:32:56]Same this much length is also going to be same as R - 6.

[00:33:01]Now, see this entire length is capital R, right?

[00:33:05]Because this is passing through the like this is from the center like the center of the bigger circle. This is capital R.

[00:33:10]This much length is going to be R - 8.

[00:33:16]And similarly, if I'll talk about this, this is nothing but the radius of the bigger circle.

[00:33:22]So, we do have like the intersecting chord segments in terms of capital R.

[00:33:28]So, we know the theorem like if there is a circle and the chords intersect, then the product of the segments are equal. So, I can write like R into R - 8 R into R - 8 is equal to R - 6 into R - 6.

[00:33:46]Right?

[00:33:47]So, if I'm going to use this, we'll be getting an expression.

[00:33:53]Like this would be R - 6 whole squared.

[00:33:55]Now, I can solve for this equation.

[00:33:58]And if I'm going to solve for this equation, I'll be getting the value of R at capital R is going to be 9.

[00:34:06]Capital R is 9.

[00:34:09]You can solve for the value of small r then.

[00:34:12]See how how capital R and small r related.

[00:34:16]This is R small r and this is also small r. So, this entire diameter is going to be 2 R + 8 which is which is the diameter of the bigger circle. So, it is diameter of the bigger circle and the diameter of the bigger circle can be written as 2 R 2 capital R. Right?

[00:34:34]So, therefore capital R we have already solved for capital R.

[00:34:38]Substitute it here. 2 * 9 = 18.

[00:34:42]8 will get subtracted. 2 R is going to be equal to 10 and therefore R is equal to 5.

[00:34:48]So, the radius of the small circle is 5.

[00:34:52]Right?

[00:34:53]So, using the intersecting chord theorem, it's very simple. I you can see that. We need not to frame like frame the side calculate the side length for individual uh this like triangle. If I'm going to mark the triangle, this is another approach. We can find the side and using the Pythagorean theorem, we can solve for it. But I have used intersecting chord theorem. I solved for R and now R we have the values of both radius, bigger one and the smaller one.

[00:35:19]Now, to calculate the area, I need to subtract the area of the smaller circle from the bigger one. So, it's pi 9 squared pi is 81 pi pi 5 squared which is going to be 25 pi.

[00:35:31]So, 81 - 25 pi is going to be 56 pi. 56 pi is the correct answer for the shaded region area.

[00:35:40]I hope it is clear to everyone.

[00:35:44]56 pi. Phoenix, you guys were correct.

[00:35:46]Shubham Sancheti, correct.

[00:35:50]Mhm.

[00:35:52]All right. Mintu, 88 pi is incorrect. I hope it is clear, guys.

[00:35:57]56 pi is the right answer. So, if it is clear, we can move to the next.

[00:36:09]Shall we move to the next, guys?

[00:36:14]Siddharth is saying yes.

[00:36:17]Okay.

[00:36:20]Let's have the next one, guys.

[00:36:23]Let's have this.

[00:36:27]Again, we need to solve for the shaded region area.

[00:36:30]Give your answer along with the correct approach. You can see two triangles are already given to you.

[00:36:36]Uh let me just uh fix the screen first of all. Yeah, this is visible now.

[00:36:41]We need to solve for the shaded region area.

[00:36:46]Take your time. Think about it.

[00:36:57]Give your answer along with the correct approach.

[00:37:30]Only 9 and 6 given. Yes, these two side lengths are only side lengths which are given.

[00:37:44]A random is here who's saying 27.

[00:37:48]But again, guys, Shubham is also saying 27. Guys, give the explanation.

[00:37:54]Give your explanation for this.

[00:38:00]Shubham, I got your answer like but if it is 27, you guys need to give the explanation. Random has given the explanation already.

[00:38:07]Math is fun is also saying 27.

[00:38:15]Phoenix is also saying 27. Okay.

[00:38:27]Everyone knows that we are going to use the property of the similar triangles here.

[00:38:32]Okay.

[00:38:33]27 27. Math is fun is also saying same.

[00:38:36]Okay, guys. Let's see.

[00:38:38]If I'm going to Let's see if I'm going to mark the side like this side length of the bigger triangle, this triangle as X.

[00:38:47]And let me just mark this side as Y.

[00:38:50]Right? Now, we know these two triangles are similar triangles. Like this triangle is similar to this one.

[00:38:56]Because the corresponding angles are equal these This is 90. This is also 90.

[00:39:00]These two angles are also equal.

[00:39:02]Right?

[00:39:03]So, this is similarity and using the similarity, we can say like these two triangles are similar. Corresponding angles are equal. And if the corresponding angles are equal and the triangles are similar, so we do have a property for the similar figures that we can write the corresponding side of the similar figure in same proportion.

[00:39:20]I can write the corresponding side in ratio. So, therefore I can write like 9 upon Y like 9 upon Y is equal to this X upon 6.

[00:39:33]And if I'm going to cross multiply, I'll be getting XY as 54.

[00:39:38]I'll be getting X into Y as 54.

[00:39:41]Now, see if I'm going to calculate the area of the triangle only, this is nothing but the base of the triangle. It is an obtuse triangle.

[00:39:51]And this Y would act as a height or we can say altitude for this triangle. This is the height, all right?

[00:39:57]This is an obtuse one, so we can this height or altitude is height of this triangle altitude of this triangle would lie in the exterior region. So, Y is nothing but the height of the triangle, so therefore area of the triangle is going to be half into X into Y. Half into base into height.

[00:40:13]It's going to be XY by 2. We already have the XY value, so which is 52. So, the area is going to be XY by 2, which is going to be 54 by 2.

[00:40:23]That is 27.

[00:40:25]So, 27 is the right answer. I hope it is clear to everyone of you guys.

[00:40:35]Yes, we need not to calculate the side.

[00:40:36]I haven't calculated the side Phoenix also.

[00:40:39]I'll just name that as X or Y and directly I form found an expression for X into Y.

[00:40:47]You can see that.

[00:40:52]Math is fun had did the same also.

[00:40:54]Phoenix, Shubham, Sheila, Mintu, you guys has given the correct answer.

[00:41:01]I hope it is clear, guys.

[00:41:05]If it is clear, we can move to the next.

[00:41:19]Shall we move to the next, guys?

[00:41:27]Okay.

[00:41:29]Just give me a minute.

[00:41:33]Let's have this. We need to solve for the value of X.

[00:41:38]>> [snorts] >> I've discussed this problem earlier also and this is a good one.

[00:41:46]We need to solve for the value of X. I hope everything is visible.

[00:41:51]Take your time, think about it. Give your answer along with the correct approach. There are multiple approaches to this one also.

[00:42:17]Solve for the value of X.

[00:42:28]Yes, Sheila, you can use Shubham is so quick with the answer, but we do need the explanation also.

[00:42:45]>> [snorts] >> By tan 2 theta, okay.

[00:42:52]Let's see.

[00:42:54]Let's just wait for few more participants.

[00:43:13]Anyone else?

[00:43:44]That is theta.

[00:43:47]This is theta and another is 2 theta.

[00:43:51]Theta and 2 theta.

[00:43:59]4 root 6 upon 4 root X by 23. So, X is going to be 23.

[00:44:05]Okay.

[00:44:07]All right. I'll give the explanation, guys. See here.

[00:44:11]Now, you can see that you guys everyone are using tan 2 theta here.

[00:44:19]But tan 2 theta is not understandable by everyone because maybe there are few users who are not from grade 10th even. They are from grade 8 or 9.

[00:44:30]Right? So, we can use the basics.

[00:44:34]We'll use the basics only. Let's focus here.

[00:44:37]If I focus on this triangle, this is theta.

[00:44:43]I can solve for this angle. This is going to be 90 minus theta.

[00:44:47]Right?

[00:44:48]Definitely using the angle sum property because this is 90. This is theta.

[00:44:52]We can solve for this angle. This would be 90 minus theta.

[00:44:56]Similarly, if I'll see, this is a right angle. This is 2 theta.

[00:45:01]We can solve for this particular angle.

[00:45:04]And that would be 90 minus 2 theta.

[00:45:08]Now, this is 90 minus 2 theta. This is theta. If I'm going to combine them, that would be 90 minus 2 theta plus theta. So, this will become 90 minus theta only.

[00:45:18]Right?

[00:45:19]If I'm I'm talking about this entire angle, this if I'll combine all of this, because this much is 90 minus 2 theta.

[00:45:26]That was is theta, so combining them, it would be 90 minus theta only.

[00:45:32]Now, you can see that this is 90 minus theta. This is also 90 minus theta, which mean the base angles of this triangle are equal.

[00:45:39]Therefore, these two sides must be equal.

[00:45:42]Like these two sides must be equal. We can see that this is X plus 2.

[00:45:48]This is X plus 2. So, this is also going to be X plus 2.

[00:45:51]Right?

[00:45:53]So, we'll focus on that later. Let's come back to this triangle again.

[00:45:57]You If I'm going to use the Pythagorean theorem in this triangle, I can solve for this side length. This is going to be H. Right? Let's name it as H and apply the Pythagorean theorem.

[00:46:05]You will be getting it as root of 96.

[00:46:09]Don't simplify this because we need it as it is. Like keep it as it is only.

[00:46:13]Root 96. Now, let's see this triangle.

[00:46:16]We can use the Pythagorean theorem.

[00:46:18]We do have this side. This side is also given. This side is also there.

[00:46:23]So, we can apply the Pythagorean theorem. So, it's going to be X plus 2 squared is equal to X squared plus root 96 squared, which is going to be 96 only. I'll write 96 directly.

[00:46:34]And if I'm going to simplify this further, I'll be getting like X squared plus 4 plus 4 X. X squared X squared will get cancel out. This 4 will get subtracted. We'll be getting 4 X is equal to 92.

[00:46:47]Dividing both side by 4, I'll be getting X as 23. So, this is the simplest approach.

[00:46:54]Like we we can't say the simplest approach, but it's the good one like understandable by everyone like for the grade 7th also.

[00:47:02]They can understand this. If they know the Pythagorean theorem, they can understand this.

[00:47:07]So, I hope it is clear, guys.

[00:47:12]Second approach is already mentioned by Sheila and uh Shubham.

[00:47:18]Tan 2 theta.

[00:47:23]Guys, if it is clear, we can move to the next.

[00:47:32]Why the side? Because I have Look, I have said like this is 90 minus theta.

[00:47:37]This was also 90 minus theta.

[00:47:40]Which means the triangle having two base angles are equal, right? Therefore, these two sides must also be equal, no?

[00:47:46]So, this side length is equal to this entire side length.

[00:47:50]Now, see this one is this up to here it is X and this is 2. So, the entire side is going to be X plus 2, no?

[00:47:58]So, if this is X plus 2, this would also be X plus 2.

[00:48:04]Right?

[00:48:09]Yep.

[00:48:11]Mintu is saying there is another simple method. There are multiple approaches, guys. But the thing is I need to give the explanation so that every single user who is watching it, they can understand it from very basics.

[00:48:25]Right?

[00:48:26]So, we'll move to the next. I hope it is clear.

[00:48:29]Welcome, friend. Let's have the next one, guys.

[00:48:33]Let me give you this one.

[00:48:37]You need to solve for the red region area.

[00:48:40]And give your answer in terms of pi only. Don't give your answer in decimal.

[00:48:52]Take your time, think about it.

[00:48:54]Let's see how many of you can answer this.

[00:49:45]>> Okay, Sheila is There Sheila and Dark Fang has given their answers already.

[00:49:51]We'll see if Sheila is correct or Dark Fang is correct.

[00:49:55]And let's just wait for few more participants to give the answer.

[00:50:00]Solving for the red region area. Random is also saying like two square root 12. Okay.

[00:50:11]Shubham 8 pi by 3 minus 4 root 3. Black Avenger Dark Fang. Okay. Dark Fang has corrected himself.

[00:50:22]Okay, let's see if it is they are correct or not.

[00:50:28]Look, if this is 30, this is the angle made by this arc like at the circumference, then the angle at the center is going to be double of it, so this is going to be 60.

[00:50:38]Right?

[00:50:40]If I'm going to see now like this is 60 and these two sides are the radius of this triangle only. If I've considered this triangle, these two side lengths are going to be equal. Therefore, these base angles must also be equal.

[00:50:53]Now, in this case, they are going to be 60 only, right?

[00:50:56]Because we are left with the sum 120.

[00:50:58]So, 60 60 and 60. And as soon as I wrote all of the angle as 60, this is nothing but an equilateral triangle. I will realize that. Right? So, equilateral triangle is here. Give me a minute.

[00:51:12]Yeah, this is an equilateral triangle whose side is already given. This is four, so this must also be four.

[00:51:18]Now, we can see we do have a sector whose central angle is 60°.

[00:51:26]And these sides are four.

[00:51:29]Correct?

[00:51:31]So now we can solve for the red region area. I need to subtract the area of the triangle from the area of the sector.

[00:51:37]What is the area of the sector? Area of the sector is theta by 360, which is 60 by 360. It's going to be 1 by 6 of the circle, which is pi r squared. 1 by 6 pi r squared, where radius is four only.

[00:51:49]And I do need to subtract this triangle out of it out of the sector.

[00:51:53]Right? So, what is the area of the triangle, which is an equilateral triangle? It's root 3 by 4 side squared. This is the formula.

[00:52:00]Where side is four only, four squared.

[00:52:02]If I'm going to simplify, this would be 16 by 6. 16 by 6 on simplification will give you 8 by 3.

[00:52:10]And this will become 4 root 3 on simplification. So, 8 pi by 3 minus 4 root 3 is the right answer.

[00:52:21]I hope it is clear, guys.

[00:52:23]8 pi by 3 minus 4 root 3. You guys were correct.

[00:52:31]Welcome, Shubham.

[00:52:33]All right, guys. We'll have the last question.

[00:52:37]I'll give you the last one.

[00:52:49]Okay, Finn. I hope it is clear. Your doubt is clear now.

[00:53:00]Vibes is hi.

[00:53:06]Just a minute, guys.

[00:53:09]I need to select a good question now.

[00:53:19]Welcome.

[00:53:42]Let's have this.

[00:53:49]We need to solve for the blue area, which is the area of the square only.

[00:53:57]Guys, be quick.

[00:54:04]Let's see how many of you can answer this and let's see who is going to give the answer first.

[00:54:21]Yes, you can use Dark Fang is saying 61.

[00:54:36]Okay.

[00:54:38]As usually, we'll see if it is 61 or not later. Let's just wait for few more participants to give the answer, guys.

[00:54:56]61 squared by 2.

[00:54:59]Now, Dark Fang is saying 61 by 2. Guys, why you are always keep on changing your answer like every time.

[00:55:09]Kano 61 by 2.

[00:55:16]Black Avenger is again with the great explanation, 30.5.

[00:55:21]61 by 2 or 30.5 means the same. Let's see if it is 30.5, guys, or not.

[00:55:27]First of all, let's see if this is OB.

[00:55:28]This is eight. This is given to you like this length is eight, which is which does mean like this is a point on x-axis. It is eight. Therefore, the if I'm going to write it in coordinate form, this is going to be 8,0.

[00:55:42]And using the distance formula, I can solve for this diagonal of the square, which is nothing but distance formula. I can solve for the diagonal, right?

[00:55:50]The diagonal is going to be like 8 minus 2 is going to be 6 squared and we have 5 squared. 6 squared plus 5 squared, it's going to be 61.

[00:55:58]Which means root 61. The the value of the diagonal using the distance formula, it's going to be root 61.

[00:56:04]Now, see.

[00:56:05]Root two side is the formula for the diagonal of the square.

[00:56:09]And the diagonal length is we have calculated as root 61.

[00:56:13]What is the area of the square? Area of the square is side squared. So, we need side squared here. I will square both sides. If I'm going to square both sides, this will become two side squared and this will become 61.

[00:56:24]Therefore, side squared is going to be 61 by 2 or we can say 30.5.

[00:56:29]So, side squared is nothing but the area only. Therefore, area is 30.5. 30.5 is the right answer.

[00:56:37]Yes, Dark Fang, your second answer is always correct.

[00:56:40]So, 25 point is not the correct answer, Mintu. I hope it is a typo error.

[00:56:46]30.5 is the correct answer, guys. I hope it is clear.

[00:56:53]Yes, Mintu, you are right now.

[00:56:56]All right, guys. So, let's call it a day. This was the last question. I hope you enjoyed the session. I'll see you tomorrow at the same timing. Till then, take care. Bye-bye.

[00:57:04]Have a good day ahead.

[00:57:05]Good night.

[00:57:11]Thanks for joining, everyone.

[00:57:13]Bye, Sheila.

[00:57:26]Yes. Yes, Finn, it's every day same.

[00:57:30]Uh yes, uh we are off on Saturday and Sunday, but it doesn't matter like sometimes I am available also, but if I'm going to upload a video on Saturday, like long format video, then I am not going to take any session on Saturday.

[00:57:47]That's how it work. And for Sunday, it is off for sure.

[00:57:55]All right, guys. Bye, Siddharth.

[00:58:01]Welcome, Finn.

[00:58:07]Bye, Phoenix.

[00:58:11]All right, guys. I'll see you tomorrow.

[00:58:12]Have a good night. Bye. Bye, everyone.