Geometry LOVERS 🤍| Can You Solve This ? | CONSTRUCTOR #youtubelive

Added: 2026-06-02

[00:01:24]Let's have this guys. This is the very first question for today. We need to solve for the value of X. It is given that AB is par to CD. Few of the angles are marked already.

[00:01:36]And using this much of information you are going to solve for the value of x.

[00:01:40]So take your time, think about it. And let's see how many of you can do this.

[00:01:45]Give your answer in the comment box.

[00:02:35]Guys, anyone with the answer for this one?

[00:02:40]This is so easy. Be quick with this one.

[00:02:41]We are solving for the value of six.

[00:02:50]Hi Sushila. Hi Yuko. Thanks for joining.

[00:02:55]We need to solve for the value of x.

[00:02:58]Give your answer along with the correct explanation for this one.

[00:03:02]Once you are going to give the answer for this, then we'll move to the next Hi Duck. Thanks for joining.

[00:04:15]That's great. I hope you're doing great.

[00:04:29]Guys, anyone with dance for this?

[00:04:44]All right. Sushida is saying 20.

[00:04:50]Yuko is also saying the same.

[00:04:53]Okay. Let's see if it is 20 or not.

[00:04:55]Guys, first of all, see this angle is 3x we know and this is 2x. This is given to us right? If I'm going to draw a line from here from point M which is parall to this side AB and this CD also then this angle is going to be equal to this because they are corresponding angles right this is going to be 3X. Similarly as these two lines are parallel this is 2x so this is also going to be 2x. So we can see that this entire angle is going to be 3x + 2x which is going to be 5x and 5x is equals to 100 and therefore x is going to be 20. So 20 is the right answer. Yuko and sushila you guys were correct. We'll have the next one. Let's have this one.

[00:05:41]Let's see how many of you can do this.

[00:05:43]We need to solve for the shaded reason.

[00:05:45]Here we are going to give your answer in exact form like in terms of pi.

[00:05:53]So take your time, think about it. Let's see how many of you can do this.

[00:06:00]We need to solve for the shaded area.

[00:06:03]Give your answer in terms of five.

[00:06:06]Take your time and give your answer along with the correct approach.

[00:06:41]Anyone guys? Anyone with the correct answer for All right, Yuko. I'm waiting for your answer. Don't worry.

[00:08:37]All right. So, Sheila is saying 8 pi + 16. U is also saying the same 16 + 8 pi.

[00:08:43]Let's see guys if it is correct or not.

[00:08:46]See this is nothing but the radius only.

[00:08:49]Right? Radius is already given to us.

[00:08:51]Radius of the circle is given to us as four. If I talk about this right this is going to be 3x4 of a circle right because this much portion is nothing but a square only so if I'll calculate this much shaded area this is 3x4 of a circle which means 3x 4 pi r² radius is already there so I'll substitute four here so 4² and if I'm going to solve this this is going to be how much 12 pi so this shaded region area is 12 pi But however I do need to calculate this reason also. Now for that what I'll be doing I'll solve for the area of this entire square and out of the square I'll subtract this quadrant. Correct? So the area of the square is going to be the side of the square which is side square side square is 4 square which is going to be 16 minus area of the quadrant it's going to be p<unk> r² by 4 here radius is 4 only. So<unk> 4² by 4 and on simplification this will become 4 pi right so we have this 16 - 4 pi for this region and this is 12 pi and if I'm going to combine them together the total area is going to be 12 - 4 it's going to be 8 pi so it's 16 + 8 pi or we can say 8 y + 16 so yuka and sushila you were correct So we'll move to the next then let's have give me a minute the surface we need to solve for the shaded is an area.

[00:10:51]Take your time. Think about it. Let's see how many of you can do this.

[00:10:56]You're going to give your answer in exact form that is in terms of pi Guys, anyone with the correct answer for this?

[00:12:01]We are solving for the shaded Yeah.

[00:12:32]Guys, give your answer in terms of I only Guys, anyone?

[00:13:42]Okay, Yuko is saying 50 pi. Anyone else with the same answer or any different answer?

[00:14:05]Okay. So, Sheila is also saying the same. Let's see guys if it's 50 pi or not. First of all, what we can do? We can solve for the area of this entire circle. Right? The radius of the bigger circle is going to be 5 + 5 10.

[00:14:23]Just a minute.

[00:14:30]Yeah, it's fine. So, the radius of the bigger circle is going to be 5 + 5 10.

[00:14:35]So the entire area of the bigger circle this entire circle it's going to be p<unk> r² which is p<unk> 10². So p<unk> 10² is going to be 100 pi. Now out of this entire area we do need to subtract this semicircle and this semicircle because these two semicircle are identical.

[00:14:56]So together they can form a circle right? So I'll subtract a circle for this minus p<unk> r² where the radius of this semicircle is 5 only. So it's<unk> 5² minus I need to subtract this quadrant also. The radius of this quadrant is also going to be this 5 + 5 10 right. So what is the area of the quadrant? It's p<unk> r² by 4. So it's<unk> 10² by 4.

[00:15:24]Now on simplification this will give me 25 pi. And similarly the area of the coordinate is also going to be 25 pi. So 100 - 25 - 25 is going to give me 50 pi as my final answer. So 50 pi is the right answer. So Sheila and Yuko, you guys were correct. We'll have the next one. Let's have this.

[00:15:47]We need to solve for the value of x, guys. Let's see who is going to give the answer first.

[00:15:55]O is the center of the circle and you are solving for the value of x. Be good with this one.

[00:16:00]This is from circles.

[00:16:42]Guys, anyone with the correct answer for this? We are solving for the value of A.

[00:16:51]Hi there. Thanks for joining.

[00:17:02]I can't understand what you are writing.

[00:17:05]If you could write in simple mathematical terms or English then it's great.

[00:17:30]Anyone guys we're solving for the value of x give your answer along with the correct approach. Be quick with this.

[00:18:12]Guys, this is so easy. Please.

[00:19:24]Yuko is saying 90 uh yuko 90 is not the correct answer because BD is not the diameter of the circle. We know that the diameter substand right angle at the circumference that's what we know or we can say semicircle substandard right angle at the circumference but BD is not the diameter here. So it's x can't be 90.

[00:19:48]You have to think about it.

[00:20:35]It's okay.

[00:20:37]You can give it a try, guys. Anyone else?

[00:20:41]This is so easy. I was not expecting anyone or like all of you to take so much of time for this.

[00:21:35]Guys, I'm telling you that O is the center of the circle.

[00:21:40]So I don't know what's taking you so much of time and why you are taking so much of time. We are solving for the value of X. BD is not the diameter. O is the center.

[00:21:53]Give your answer please.

[00:21:56]We have taken so much of time and we are still I think five more questions are there to go.

[00:22:21]Yes, C can move around the circle.

[00:22:31]you are taking it too seriously. But this question is pretty much simple. We can use the properties of the cyclic coordinator or we can use the concept of the angle substandard at the center.

[00:22:44]There are multiple approaches to this one.

[00:23:07]All right, finally someone has given the answer like Sheila is saying 100. Let's see guys if it is 100 or not. First of all, see this U if I'll talk about this A OB triangle. This one this is definitely going to be an isocles triangle because O A and O B are equal sides of this triangle because they are radius of the same circle.

[00:23:31]Therefore these two angle must be equal.

[00:23:33]Right? So if I'm going to calculate these two angles are going to be 55 each. Let's just not focus on the triangle. Let's just focus on this angle. this 55 and this 25 together they will make an angle 55 + 25 is going to be 80°. So if this is 80 this angle x and this 80 they are the opposite angle of the cyclic quadrator. So what I can write like x + 80 is equals to 180° because we know that opposite angles of the cyclic quadillator are supplemented.

[00:24:09]So from here I'll be getting the value of x as 100°. So 100° is the right answer. So Sheila, you are right.

[00:24:17]The only person to give the correct answer for this one.

[00:24:22]Great. We'll move to the next.

[00:24:25]Let's have something else.

[00:24:29]Give me a minute.

[00:24:33]Let's see how many of you can do this.

[00:24:39]This is easy guys be quick with this. We need to solve for the value of x. Again there are multiple approaches for this one also.

[00:24:48]Solve for the value of x.

[00:26:01]guys. Anyone?

[00:26:04]This is I think very easy.

[00:26:08]Please be quick with this.

[00:26:15]All right. Ice has given the first he is the first one to give the answer.

[00:26:23]Yuko is saying 90 and Sushila is also saying the same. All right. Let's see if it is 90 or not. First of all, similarly if this is a center what we can do these two angle must be equal because these are the radius. So they are going to be 65 each. Correct? Now see these two are the interior angle of this triangle and this interior angles together is going to be equal to this exterior angle.

[00:26:44]Right? So I can use exterior angle property or you can solve for this angle and use the straight angle property here. So I can write this 65 + 65 is going to be 130 and this is equal to x + 40 because x + 40 is an exterior angle for this and using this I can get the value of x is as 130 minus 40. So it's going to be 90. 90 is the correct answer.

[00:27:11]Ice Yoko and Sushila you guys have given the correct one. Let's have this guys.

[00:27:16]Let's see how many of you can do this.

[00:27:20]We need to solve for the shaded reason area.

[00:27:28]The only code is given to you like this code is given length of the code which is a tangent to this circle. It is given length of the code is given as 16. We're going to solve for this shaded area.

[00:27:44]Give your answer in terms of five. Guys, take your time.

[00:28:36]Guys, anyone?

[00:28:39]We are solving for the shaded region area.

[00:28:46]The segment shown here is a code for the bigger circle, but is a tangent for the smaller one.

[00:29:00]Hi Victory, thanks for joining.

[00:29:48]Anyone with the correct answer? Guys, you're taking so much of time for this one. We are still I think there are two more questions to go.

[00:30:12]Ice is saying 64 again. He is the first one to give the answer. Victory is at second.

[00:30:18]64 pi. Okay, let's see if it is correct or not. Guys, let me just mark the radius of the smaller circle as R. And if I'm going to draw a perpendicular here because we know that the radius are perpendicular to the tangent at a point of contact, right? Let's see this is the radius of the smaller circle and the radius of the bigger circle is capital R. Now we formed a right angle triangle and if I'm going to use the Pythagorean theorem here I'll be getting R square minus R square is equal to this this length is 8 right because perpendicular is definitely going to biseect the four so it's going to be 8 square which is going to be 64 so we have this expression we can solve for the shaded area the shaded area is going to be pi r² minus the area of the smaller circle we can take the pi common it's going to be p<unk> R square - R square and we have this value as 64. Substitute the value here, you'll get the answer as 64 pi. So 64 pi is the right answer.

[00:31:18]Eyes in victory, you guys were correct.

[00:31:20]We'll have the next one. Just a minute.

[00:31:23]Let's have this.

[00:31:26]We need to solve for the value of X. It is given that H point H is the intersection of the medians.

[00:31:33]This is very easy.

[00:31:37]You're going to solve for the value fix quick with this All right. W three is saying eight.

[00:32:54]Yuko is also saying eight. I hope it is correct. And let's see if it is correct or not. We know if we are going to have an intersection of the median, this point is known as cent. So here h is centr and we know that centr divides the median in 2 ratio one right and the longer segment is towards the vertex. So which means this is the longer segment and this is the shorter one. We can see that also. So here this is dividing it in two ratio one. So it means that bh is equal to twice of hf. Right? So, bh is 3x + 6 and twice of hf is going to be 2 into 2x -1. And if I'm going to solve this, I'll be getting an expression like 3x + 6 = 4x - 2. And on solving this, I'll be getting the value of x as 8. So 8 is the correct answer. Yuko and Victor, you guys were correct. We'll have the next one.

[00:33:59]And the last one for today maybe just give me a minute.

[00:34:13]Let's have this.

[00:34:15]We need to solve for the shaded region area. Let's see who's going to give the answer first. For this this shaded area for the circle, you are going to give the answer in terms of five. Take your time. Think about it.

[00:34:40]Be good with this one.

[00:35:01]Uh Victory uh there is nothing in the right side like there's nothing on the right side. No, no side is marked on the right side.

[00:35:11]This much information is sufficient now. Is it visible? Thank you.

[00:35:49]All right, guys. Take your time. Give your answer in terms of five.

[00:37:02]Anyone Please.

[00:37:38]Okay, we have someone.

[00:37:44]No r = 10 into <unk>2 upon 2 - 5.

[00:37:52]No guys. Okay. You have solved for the value of r but we are solving for the shaded area.

[00:38:00]Give you a final answer for the area of the circle.

[00:38:06]However, answer is not correct for all also.

[00:38:12]Yes. Then what is your final answer for the bill value of area?

[00:38:27]Okay. Victory has given his answer 25 by 16.

[00:38:32]Anyone else?

[00:38:45]Yuko is also saying the same. Let's see guys if it is 25 pi by 16 or not. How we are going to approach for this? See the sides are already even this side is five. This is also five. Now if I'm going to drop a perpendicular from here.

[00:39:03]So what I'm going to have this side is going to be 5 - r right because this side is five and this much length is r so this will be 5 - r for sure let me just write it as 5 - r and this if I'm going to join these two centers because this is the center of the circle and this is the center of the quadrant they will have a common point of contact and they will pass from the common point of contact. So this is going to be the radius of the quadrant which is five and this is going to be the radius of the circle which is r. So the entire length is going to be 5 + r.

[00:39:44]So we have this right angle triangle here. We can apply the pythagoran theorem. So 5 + r² is equal to 5² + 5 - r². And if I'm going to expand this 5 + r or this 5 - r² the first two term which is a square and b square they will get cancel out and I'll be left with 2 a b only. So this side it's going to be 10 r as 2 a this is 25 and this side it's going to be minus 2 a. So it's - 10 r.

[00:40:13]Combining the values of r I'll be getting 20 r is equals to 25 and the r is going to be 25 upon 20 which is going to be 5x4. So we have the radius.

[00:40:24]Therefore the area is going to be p<unk> r² which is 25 by 16 pi. So 25 x 16 pi is the right answer. Victory and you go.

[00:40:35]You both were correct.

[00:40:38]I hope it is clear to everyone else. You you're welcome shusha. So this was the last question guys for today. I hope you enjoyed the session. We'll have the next session tomorrow at the same timings.

[00:40:57]Till then take care. Bye-bye. Have a good night.

[00:41:37]Bye victory.

[00:41:43]Bye you.

[00:41:50]Bye Sushila.