Math Puzzles Challenge | Brain IQ Test

[00:00:33]All right guys, this is the very first question for today. We need to call for the value of angle F here. This is angle F.

[00:00:43]So take your time, think about it. Let's see who's going to give the correct answer first. We are solving for the angle.

[00:00:50]F.

[00:00:52]Take your time. Think about it. Let's see who's going to give the correct answer first.

[00:02:09]guys. We are solving for the value of f.

[00:02:11]Please be quick with this one.

[00:03:00]Guys, it has been more than 3 minutes already.

[00:03:06]No one is there to give the answer for this one.

[00:03:09]We are solving for the value of Okay. Sudha.

[00:03:58]Sudha is the only one to give the answer till now. Sedhart is also saying 136.

[00:04:04]Okay. Let's see if it is 136. We have wasted so much of time for this already.

[00:04:08]See there are multiple approaches to this one. But I'll be using this one. If I'm going to consider this triangle I can use angle some property right and I can solve for the third angle which is angle W right now because two of the angles are already there. This 41 and this 95. So 95 + 41 is going to be 136.

[00:04:33]Correct?

[00:04:34]And if I'm going to subtract 136 out of 180, what I'm going to get? I'll be getting 44. So this is going to be 44.

[00:04:43]And I know this is this x y z and w is in cyclic coordinator. So therefore the opposite angles must be supplementary.

[00:04:53]So f + 44 is equals to 180° and therefore the value of f is going to be 136°.

[00:04:59]So 136 is the right answer. Siddhart and Sudha both of you are right. Hi Kushagra. Thanks for joining. We'll move to the next. 136 is the right answer.

[00:05:10]Let's have the next one. Just give me a minute.

[00:05:16]Let's have this one.

[00:05:22]Let's see who's going to give the correct answer for this. We need to solve for angle C E D. You can see this angle C E D. O is the center of the circle. C E D is this angle. So take your time. Think about it. Let's see who's going to give the answer for this one.

[00:05:38]Solving for angle CDO is here. Go is saying 40. Let's just wait for a few more participants.

[00:06:06]Anyone else, guys?

[00:06:45]guys. Anyone else?

[00:06:48]Only one user has given the answer for this one. We are solving for angle C D.

[00:06:54]Please be quick with this one.

[00:06:59]I'm waiting for a few more participants to answer this. Jack is here. Jackson is saying 40. Eric is saying 40. Okay, that's great.

[00:07:09]Anyone else?

[00:07:12]Siddhart is saying 30.

[00:07:16]Okay.

[00:07:17]Okay. He corrected himself to 40 then.

[00:07:20]Okay. Let's see if it is 40 or not. And let's see how we are going to solve this. Patrick is also saying 40. See guys, if I'm going to join this now, I can see like this angle is on this arc but at the circumference and this angle is on the same arc but at the center and we know that the angle subended by an arc at the center is double the angle substanded by the same arc at the circumference. So this is 50.

[00:07:47]This angle is going to be 100, right? So let me just write it as 100.

[00:07:53]Now I can consider this triangle E O C and we know this is an isocles triangle because O E is equal to OC. They are the radius of the same circle. Therefore these two angles must also be equal.

[00:08:04]They are the base angles of the isocles triangle. So what is the measure of these angle? They are going to be 40° each. Now they are 40° each. Now see we have one more thing here that this AC is parallel to this ED. Now if we have this what I can conclude that this angle is equal to this angle because they are going to be alternate interior angle. So this angle is also going to be 40°. So this is one of the approach. There are multiple approaches to this one. 40° is the correct answer. So Patrick Siddhars Eric Jackson and Coyo you guys were correct.

[00:08:43]We'll have the next one and let's have the next one.

[00:08:46]Let's see how many you can do that.

[00:08:49]Just give me a minute.

[00:08:52]Let's save this.

[00:08:55]I hope it is visible.

[00:08:58]Look what is given to us. We need to solve for the red shaded area here. This is a square for sure. This is given to us that this is a square. And this is also given that the radius of every single circle is one unit.

[00:09:16]So take your time, think about it. Let's see who's going to give the correct answer first. You need not to give your answer in terms of decimals. Give your answer in terms of root which mean you are going to give your answer in exact form.

[00:09:31]So I'm just I'm just waiting for three to five participants to answer this and then we'll move to the next. Let's see who's going to get the correct answer first.

[00:10:58]Okay, we have one user po is so quick with the answer. 12 - 82 is saying we'll see if it is correct or not. Let's just wait for few more participant. Warren is saying to guys you can give your explanation for your answer if you are going to give the different answers so you can share your explanation that how you're getting your answer or else I'm going to give the explanation soon but I'm still waiting for few more participants.

[00:11:27]Tenbo is here.

[00:11:28]is also saying the same 12 minus 8 move to Warren is saying two.

[00:11:39]Let's just wait for a few more participants.

[00:13:12]All right. So I can see so many of user has given the answer. Coyo has given the explanation also. Thanks for that. Coyo Q5M70 is also saying the same. Kishag is saying two and I'm stupid is saying 2<unk> 2 - 2².

[00:13:33]Okay, that's fine. Let's see. There are multiple approaches. You can consider the entire square also or you can draw a triangle. You can draw a triangle like this joining the centers.

[00:13:48]Okay. So, what I'm going to do, I'll be having a triangle here. Let's see. These are the centers. I'm going to mark the centers. Definitely as this square side is tangential to these circles. So they will share a common point of contact, right? So this is going to pass through this and this and this and this is going to be a right triangle for sure. And now you can see like the radius for each circle is going to be one. So this side is going to be 1 + 1, right? 1 + 1. This is going to be two. This is also going to be two. And I can solve for the hypotenuse. The hypotenuse is going to be 2<unk>2.

[00:14:31]Correct?

[00:14:32]So if I can see like this is 2<unk>2 what I can solve for this from here I know that this is one this much is also one so 1 + 1 is going to be two and I can get the side of the square let's say this is the side of the square this is s so what I can write like this 2 + s is equals to 2<unk>2 and from here that side I'm going to get it's going to be 2<unk>2 - 2. So this is the side. I can square this. So you'll get the final answer as 12 - 8 <unk>2.

[00:15:13]So the area is going to be 2<unk>2 - square or you can take the 2 common or write 4 like sorry 2 common and <unk>2 - 1 square. Right? So we have so many of users. Raja Sony is also saying 3.44. 44.

[00:15:33]Let me just read everyone comment. Give me a minute. Coyo, Coyo is correct. Ken, you are right.

[00:15:41]User Q5M70, your answer is also correct.

[00:15:47]Stupid 42069, you are also right. Pigodio, your answer is correct.

[00:15:53]Kajasi has given the answer. Yes, you are also right.

[00:15:59]So all of you has given the correct answers only two users Warren and Pushag were Singh two. I hope it is clear to you guys.

[00:16:08]So we'll move to the next. Let's have the next one.

[00:16:11]Just give me a minute.

[00:16:15]Let's have this. This is very easy guys.

[00:16:18]Be quick with this one. We are solving for the value of x here. This is the missing value. We need to solve for the value of x. Let's see who's going to give the correct answer first.

[00:16:36]Alexander uh you're saying 2<unk> <unk>2 - 1 square but we are also going to have two along with this.

[00:16:55]Now for this question, we are solving for the value of x. Guys, please be good with this one.

[00:17:10]Yes, Mr. Stupid, your answer is also correct.

[00:17:17]Guys, you can refresh your stream. We are at the next question. We are solving for the value of angle X.

[00:17:24]Be quick with this one.

[00:17:39]We have narrow. We have tienu. Both of them are saying the same. They're saying 146.

[00:17:48]Yes, narrow. Your explanation is also correct.

[00:17:53]is saying 146.

[00:18:00]Sadhhat is saying 145.

[00:18:03]Sedat is here. Dworth saying 146. Shivaju.

[00:18:15]All right. I can see most of you has given the right answer. Let's see. Uh how many sides are there? I can count the angles first of all 1 2 3 4 5 6 7 right there are seven angles.

[00:18:29]So this is a heptagon and to get the entire angle sum of a heptagon we can use the formula like n minus 2 into 180° right here n is 7. So 7 - 2 is going to be 5 and 5 into 180 will give you 900.

[00:18:44]So 900 is going to be equal to the sum of all of these angle. You can add them all and equate it to 900° and you can get the value of x. The value of x you'll be getting is going to be 146°.

[00:18:56]146 is the correct answer.

[00:19:00]So Mr. Akim and Alexander you are at the previous question. We are at the next one right now. Your answer are correct for the previous question. You can refresh our state. So for this question Mr. Shivraj coyo dart siddhart is saying 145 maybe it's made a typo error only push narrow and you guys were correct we'll have the next one let's have the next one let's see how many of can do that let's have this we need to solve for the shaded is an area in this question uh once this is a semicircle you can see and I would like to add an information like this line is passing through the center of the circle okay these lines are passing through the center of the circle definitely and this is the diameter of the semicircle you need to solve for the shaded is an area let's see who's going to give the answer you need not to give your answer in terms of decimal you can give your answer in terms of Let's see who's going to give the correct answer first.

[00:20:19]Give your final answer in terms of five.

[00:21:44]Okay, we have one user Bris DM. He's saying 4.55.

[00:21:50]We'll see if it is correct or not later.

[00:21:52]Let's just wait for a few more participants. I'm going to give the explanation. So, don't worry.

[00:22:02]Mr. Ratio, I can't understand your comment. It's not in my native language.

[00:22:16]20.5 pi co is also saying the same coyo is saying 20.5 pi draat is saying 41 by 50 41 by 50 and there is no pi is it draat you can check your answer I So you made a typo error. You can check it.

[00:23:39]anyone else guys till now only uh two user has given the answer I think Mr. DM is saying 4.55. Co is saying uh 20.55.

[00:24:00]I'm still waiting for few users to like answer for this.

[00:24:32]Okay, Kushagra is also here. Kushagra is saying we are solving for the yellow shaded area.

[00:24:46]Shagra is saying 41 pi by 2. Tienu is also saying the same 20.5. 41 pi is 41 by2 is same as 20.5.

[00:24:55]Okay guys, let's see here.

[00:24:57]See what what I can do. If I'll be seeing this, let's consider the radius of the semicircle. This semicircle is R.

[00:25:04]So this is going to be R. This length is also going to be R. And this is also R.

[00:25:11]Right?

[00:25:13]So what we can see we can see a concept of two intersecting codes here, right?

[00:25:19]Where we know that the product of the length of the segments are going to be equal.

[00:25:24]So this is r into r will give you r².

[00:25:27]This entire segment is r + 6 right? And this r + 6 is going to get multiplied with this one only. So r + 6 into 1 will give you r + 6 only. Right? So let's keep it as r + 6 only.

[00:25:43]Okay. So when I'm going to take this on another side, this will become negative r and this is also going to be min -6.

[00:25:50]This is the quadratic equation which I'm going to get. And if I'm going to solve this, I'll be getting r - 3 and r + 2 as y factors. And from here I'll be getting the value of r as 3 and minus2. But radius can't be negative. So I'll be considering the value of radius as 3.

[00:26:08]Now you can solve for the diameter of the bigger circle. First of all, this is 6 + 3 + 1. 6 + 3 + 1 is 10. Therefore, the diameter is 10. Radius for the bigger circle is going to be five. So the area of the entire circle is going to be 25 pi p<unk> r² right minus area of the semicircle which is going to be p<unk> r² by 2 so<unk> 3² by 2 will give you what this is going to be 9<unk> by2 or I can write 4.55 and if I'm going to subtract this this will give you 20 5 pi as the final answer. So 20.5 pi or I can say 41 by 2 pi is the correct answer. 41 by<unk> by 2. So Mr. P, glad coyo pushagra you guys were correct.

[00:27:07]We'll move to the next. Let's have the next one. Let's see how many you can do that. Just give me a minute.

[00:27:15]Let's solve this.

[00:27:23]I hope it is visible. We need once again we need to solve for the shaded reason area which is the entire area of the semicircle.

[00:27:41]Take your time. Think about it. We are solving for the entire semicircle area.

[00:27:48]Okay, shaded area is nothing but the green shaded area. Please be quick with this one.

[00:28:28]Guys, don't give your answer in terms of decimals. Give your final answer is in ter in terms of pi.

[00:28:36]Let's see who's going to give the correct answer first.

[00:29:48]All right, we have three users, Coyo and Kushager.

[00:29:52]Tv is saying 312.5 pi. Coyo is saying 625 by 2 pi andag is also saying the same. We'll see if it is correct or not later. 625x2 is same as 312.5.

[00:30:10]Let's just wait for a few more participant size.

[00:30:51]Okay, we have one more user saying 464 by 2. 464 means 232 pi.

[00:31:01]Okay, we'll see.

[00:31:04]Anyone else with the same answer or anything different today?

[00:31:19]Okay, we have Sedhart. Sedhart is also saying the same. Okay, let's see guys how we going to approach for this one.

[00:31:26]Let's consider the radius of the semicircle as R or I can say capital R.

[00:31:31]If I'm going to join this from center to this end, this is going to be the radius for sure. And let's consider this as X.

[00:31:41]And if I'm going to join this end to the center, this is also going to be the radius. Now I can consider these two triangle and form two different equation. I can write like r² = x² + 24² for this triangle. Right?

[00:31:56]Let me use some other color for this triangle. And similarly, if I'm going to consider the bigger one, I can get the expression for r². Again it's going to be x + 8² is equal to 20².

[00:32:11]Now we have the equation for r². I can equate both of the equations. So I can make them equal like and if I'm going to equate them I can get the value of x as 7. Now once I got the value of x as 7, let me just write it here. You can consider any of the triangle. I'm considering this one and apply the Pythagorean theorem and by doing so r is going to be the root of 24 square + 7 square which is going to be 625 right so therefore the value of r is 25 so once you have the value of radius which is semicircles uh radius only so the area for the semicircle is going to be p<unk> r² by 2 so this is going 25 pi 25 square is going to be 625 pi Okay 625 along with this we have pi and at the denominator we are having 2. So 625 by 2 is the correct answer or you can say 312.55 also. So sedhart hugh and pushadri koo tenu you guys were correct 312.55i or 625i is the 2 is the correct answer. We'll have the next one. Just give me a minute.

[00:33:36]Let's save this. Now, this is very easy guys. You need to solve for the area of the square ABCD. See, it is mentioned here. We are solving for the area of ABCD. We are not solving for the shaded area. Shaded is an area is already given to you this time. 1 cm square. Now using this much of information you are going to solve for the area of the square A B CD Matthew the correct answer is 312.55 we are solving for the area of the semicircle there I hope it is clear you can check the solution.

[00:34:28]The envo is here with the answers saying 16.

[00:34:34]Guys, we are solving for the area of the square ABC D. You can mention your approach like there are multiple approaches to this Okay. So I can see Tenbo Sadhart Kushag all of them are saying 16 Mario Angel is saying 8 cm square.

[00:35:46]Okay, we'll see guys anyone with the explanation for their approaches because this question can be done by multiple ways.

[00:36:04]PW is also saying 16.

[00:36:07]Q5 M70 is also saying 16. Okay, all of them are saying 16.

[00:36:15]C there is one approach we can solve for the side of the square. Okay. Or the another one is going to be like I can divide the entire figure in 16 equal part.

[00:36:31]Okay. So what I can do if I'm going to draw this if I'm going to do this I'll be having 16 equal 16 congrent triangles here okay so you can count the number of triangles This is 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 16 triangles are there. And for one triangle the area is already given. So it's going to be 16 cm square. This is one of the approaches. Or else you can see that this is a right triangle. This is an isocles right triangle. This side is one. This is one. Right? You can solve for this. This is also going to be one.

[00:37:34]Correct? If this is one, this is also going to be one. You can solve for this side.

[00:37:41]Sorry, this is not one. The area is one.

[00:37:44]Right? If the area is one, this is going to be <unk>2 <unk>2.

[00:37:50]Correct? So, this entire length is going to be 2<unk>2, which is the hypotenuse for this smaller triangle. You can solve for this side length. They are going to be two each. Right? Now if this is two, this is also going to be two. Therefore, the side of the square is going to be four. So once you got the side, you can solve for the area directly. Four square is going to be 16.

[00:38:16]Okay.

[00:38:17]So how many user has given the correct answer? Yu coyo Siddhart pushag PW Q5 M7 16u is saying 16 it's 16 but I can't prove it without just moving the geometry okay yes Mario your answer is now correct 16 is the correct answer guys we'll have the next one just give me a Okay.

[00:39:15]I hope it is visible guys.

[00:39:18]Jerry, your answer is correct. 16 is the right answer.

[00:39:22]We are at the next question. We need to solve for the missing region area.

[00:39:28]We are solving for this reason area.

[00:39:31]So take your time. Think about it. It is given that all of these boxes are squares only and the side of all of the three sides for this triangle is are equal. So therefore this is an equilator triangle. You need to solve for the shaded is an area.

[00:39:49]Okay take your time think about it.

[00:39:51]Let's see who's going to give the correct answer first. You are going to give your answer in terms of like root or uh here we are not going to have any pi. Right? So you are going to give your answer in terms of roots. Don't give your answer in terms of decimals.

[00:40:07]Be quick with this one.

[00:41:16]Mr. Clinky 7237 saying 72. uh but 72 is not the correct answer and even even if you are getting 72 you can share your approach or give your explanation for the answer.

[00:41:30]At least share your approach that how you are thinking about the problem. What is your approach for this one?

[00:43:16]All right. We have Dra saying 85.93.

[00:43:22]Okay. He has given the entire answer in decimals.

[00:43:25]I envy saying 6 49.61 <unk>3.

[00:43:31]All right. Let's just wait for a few more participants. Then I'm going to give them final explanation and answer for this for sure.

[00:43:40]I know they are also solving. So let them take their time.

[00:45:07]Guys, what happened? Is there no one to give the answer for this one? Only two years has given the answer till now.

[00:45:18]Anyone else with the same answer or any different answer?

[00:45:23]Please be quick.

[00:45:30]S is going to be 11 square<unk> 2. S is not 11 <unk>2 by the way.

[00:45:42]121 <unk>3x 4. Okay, it's okay. I'll keep it in mind. Then we'll see if it is correct or not.

[00:45:53]171.85 85 PW guys everyone is giving different answers you can check your logics I'll give you one more minute one to two more minutes latino is is this 121 <unk>3 by 2 is the final answer for like final answer for the area of the shaded Is it Mr. Bobo wax is saying 36 into 5 to power 1 by 2 strange we see I'm going to give the explanation for sure cactus 09 a few minutes earlier is 16 okay for the previous question Eddie yes for the previous question it's 16 your answer is correct for the previous one all right guys I think I had given you enough time for this one let's have a look see now look at the vertex here like this is the vertex I'm going to consider this I'm going to drop the straight line from here what is the height of this line this is going to the side of the square which is two this is going to be the side of the this square is going to be three right and this is two so this entire length is going to be of five units right I'm highlighting it and writing it as five this is five unit now see this is nothing but the side of the square which is two and the side of this square is going to be six so this is two so what I'm going to get this is going to be this is going to be 6 - 2 this is going to be four Okay. So what we are going to do I can solve for this length let me just name it as something let's say some variable I'm using X here I'm writing X for this much length and I'll be considering this as Y. Okay.

[00:48:17]So what I can do I can solve for the value of X using the Pythagoran theorem.

[00:48:21]It's going to be 5 square + 4 square and square root of that. So square root of 5² + 4 square will give you x the value of x you are going to get is going to be<unk> 41 right so x is roo<unk> 41 because 25 + 16 is 41 okay so we have the value of x I can write the value of x here as roo<unk> 41 so I have this this was x now from here to here this is y right I can solve for the value of y but how I'm going to do so I can use the similarity.

[00:48:55]These two triangles are going to be similar to each other because the these corner angles are equal and the corresponding angles are equal for these triangles. So if this length is six definitely because the side of this this square is going to be six. I can write the corresponding sides in same proportion and solve for the value of y.

[00:49:15]Right? So what I can write like y upon<unk> 41 is equ= to 6 upon 5 and from here I'll be getting the value of y as 6x 5 <unk>41 and now let's I'm raising everything what is the value of the side of this triangle this is going to be y + roo<unk> 45 41 or I can say x + y right I have everything now I can add them like I have x I can add this to get the side x + y. x is roo<unk> 41 + 1. So the side length I'm going to get is going to be 5<unk>41 + 6<unk>41. It's going to be 11<unk> 41 by 5. This is the side of the triangle.

[00:50:06]Now once you have the side of the triangle you can solve for the area because this is an equilater triangle and for equilator triangle the area of the square is given by the formula that <unk>3x4 side square this is side I am going to square this directly and I'm writing it here squaring this 11 square is 121 roo<unk> 41 square will become 41 and square of 5 will become 25 now this 25 into 4 will become from 100 only. So I'm writing it as 100.

[00:50:39]This is going to be 4961 and writing it in decimal will give you 49.61 <unk>3 as your final answer for the shaded area. So I hope it is clear 49.61 or if I'm going to convert it in entirely in decimal it's going to be 85.93.

[00:51:03]So two users has given the correct answer. P PW has corrected himself later. PWS your answer is correct. Enbo you are right. And one more user Dworth.

[00:51:15]Dworth was the first one to give the answer for this one. So they were worthwh you guys were correct.

[00:51:23]And one more user were there. I forgot his name. Just give me a minute. Mr. Johnny John Young sorry your answer is also correct.

[00:51:37]So I hope it is clear to everyone now.

[00:51:43]Yes Denvu PW and John you guys were correct for this question.

[00:51:56]All right guys, so this was the last question for today. I'll see you tomorrow at the same timing. Uh, tomorrow is Saturday. No, I'm not going to see you tomorrow. I'll be seeing you now on Monday directly.

[00:52:07]Till then, take care. Bye-bye.

[00:52:10]Have a good day. Good night.

[00:52:13]I'll see you on Monday at the same timing, 7:30 p.m.

[00:52:36]Bye at the end. Have a good night.

[00:52:53]Bye. Sedat by Kushagra. Good night. All right, guys. Have a good night. I'll see you on Monday.