A Nice tricky geometry math question .

This math question contradicts geometry or I think contradicts geometry. Watch to the end and see why I said so or why I am wrong as well. Welcome back to my channel. Today we have a lovely geometry math question to solve. So this is not drawn to scale and it's a freehand sketch. So we have a circle and inside it is described a quarter circle. So this is a quarter circle and the radius of the quarter circle is 4. So we are asked to find the area of this big circle. Okay first things first, since we are told that the radius of the quarter circle is 4, let's call this a, b and c. So like I said watch to the end and see if the answer we got is geometrically right or wrong. Okay so first of all since bc is equal to 4, ab is also equal to 4. The reason is that both are radius right. Both are radii. They are both the radius of a circle which is the quarter circle here. Now because this is 90 degrees, because this is 90 degrees, that simply means that ac joins at the center or ac is the diameter of this big circle. I will please manage that. So it means that ac passed through the center of this circle and ac is the diameter. Now why? Remember our circle theorem that states that in a circle and this is your diameter, the angle formed in the semicircle is 90 degrees right. So angle formed in a semicircle is equal to 90 degrees. This is Bell's theorem. So whenever you inscribe a triangle and one of those angles is a right angle, it simply means that one of the legs is actually the diameter of the circle. So definitely ac is the diameter of the big circle. Now having done that, we now have triangle abc. Okay so this is it. So we now have triangle abc. Now let's draw it out. So this is a, this is b and this is c. So this is a right angle and we have ac as the diameter. I know the diameter is what? 2r. Now where our r is the radius of the big circle. So the radius of the big circle is r. Now here is 4 and here is 4 as well. I've explained why here. So using Pythagorean theorem, using Pythagorean theorem, we have that ac squared is equal to ab squared plus bc squared. So solving further, we are going to have ac squared that is 2r squared is equal to ab squared 4 squared plus bc squared 4 squared again. So 2 squared, so this sentence 2 squared multiplied by r squared is equal to 16 plus 16. So 2 squared is 4. So we have 4r squared is equal to 32. Now let's divide both sides by 4. So we divide here by 4, divide here by 4, 4 will remove 4. So we have that r squared is equal to 32 divided by 4 which is 8. So let us finish with it. So we have that r squared is equal to 8. So this implies that r is square root of 8, right? Now square root of 8 is the same thing as square root of 4 multiplied by 2. So we can go ahead and I'm going to clean everything here because I don't think we need them again for anything. This is why I normally have a second rack that is a bit wet. But since I don't have any now, I don't want to cut this video. I don't really want to cut this video. Now, if this is the first time you are coming across this video, this channel, please hit the subscription button, turn on your notification bell so that you don't miss our videos. We upload our videos as often as possible. Do tune in at your convenience. There must be something for you to watch. Now give us a thumbs up if you love what we are doing, okay? Alright, thank you. So looking at this now, looking at this, this is what we have. So this can be written as square root of 4 multiplied by square root of 2 is equal to r. So we now have 2 root 2 is equal to r. So we have found the radius of the big circle. Now, we are asked to find the area of the big circle, right? Now area of a circle is pi r square. Sorry, my video wasn't even recording my voice. So I had to cut off that part. Now we are at the place that the radius is 2 root 2, okay? I remember that we are asked to find the area of this big circle. Now the area of this big circle, area of a circle generally is pi r square, okay? So area of the big circle is pi multiplied by r. r is 2 root 2, right? All squared. Then our area will be equal to pi bracket. If we solve this, we are going to get 8 back. So no need of 2 squared is 4 root 2 squared is 2. 4 times 2 is 8. We get this back. Now pi is equal to 3.142. So area is 3.142 multiplied by 8. Now you are going to tell me the answer we got. Is it really what it's supposed to be? So we have, this is going to give us 24, 25 points. So let's say it's 8 times 3 is 16, carry 1. 8 times 4 is 24, 32 sorry, plus 1, 33. We carry 3. 8 times 1 is 8, plus 3 is 11, write 1, carry 1. 8 times 3 is 24, plus 1 is 25. So we have 25.136 units squared. Now this is what our area is showing us. But this is not my issue. The issue I have is, is it possible that the radius, we are told that the radius of this smaller circle is prime, that part of it is inside this circle, is 4. The radius, let's call it small r, is 4. And we are told that this big circle, from what we found, the radius is equal to what? 2 root 2, which is not even up to 3, because square root of 2 is not up to 3. It's not up to 1, right? Yeah. So this is about 2 point something, 2 point something. So is it possible that the smaller radius is bigger than the, is smaller than the bigger radius? Sorry. Is it possible that the smaller radius is bigger than the big radius? That is, the radius of the circle we have part of it in this circle is bigger than the radius of the main circle. So that is it. I was dragging it to somebody and I want to know your opinion. Is it right or wrong? Okay. I mean, the comments I'll be reading, because for me, I'm here to learn. Tell me what you think. Is this mathematically right? Algebraically it is right, but geometrically wise, is it really right? And I did not even take out time to actually construct, like, draw the circle using scale. I didn't. As soon as I did, I didn't. I want to bring it for you people to tell me if it's correct or not.