Can YOU Solve This? – Math Geometry Puzzle

Added: 2026-05-14

[00:00:00]Hello my lovelies. It's Zenna and today I want to show you how to solve this problem where we have to find the radius of the circle. We have our circle here.

[00:00:12]We are given the length of this part here that goes through the center of the circle. We are given the length of this part here. And they tell us that we have a right angle here. And we have to find the radius of the circle. So the radius always goes from the center of the circle to the edge. So this is my radius. But the question is, am I going to use this radius here that I just drew or is maybe this radius better or maybe this radius? So which one should I pick?

[00:00:48]And usually when you want to solve such problems, always look for uh lines that touch your circle or that intersect your circle. And here we have a line that intersects my circle here.

[00:01:05]And here we have a line that intersects my circle here. So I'm going to use these points here. So from the center to this point here, this is my radius. And from the center to this point here. So also this here is my radius.

[00:01:26]Okay. So now we've created a triangle here which is also a right triangle which is perfect for the Pythagorean theorem. We know the length of this side here. But what about the length of this side here? How long is this part?

[00:01:47]Well, we only know the length of this entire side here, which is of length eight. And we know that this part here is my radius.

[00:01:59]So for only this part here, I can take the entire side first, which would be too long. But if I just subtract this part here, then only this part here is left. And this is what I'm interested in. So I take the entire side, the eight, and then I subtract my radius and then this is what is left.

[00:02:30]Okay. So now we can use the Pythagorean theorem here in this triangle. For this we first have to find the hypotenuse.

[00:02:38]That is always the side that lies across my right angle. So this is the hypotenuse.

[00:02:45]And the Pythagorean theorem then says take one of the sides, so the four and square it plus take the other side and square it. So I take the 8 minus r, write it in parentheses and square this entire thing and then you get the hypotenuse squared which is my r squared. In this case and now we only have to solve this equation for r. We have 4^2ar which equ= 16.

[00:03:22]Let's take this equation to a new page here and let's solve this equation for r. Now maybe we first get rid of these parentheses here. We have a difference in our parentheses and we square this thing. This is a special product and we can use a formula to get rid of these parentheses because every time you have something like a minus b and then you square this then you get the following as a result a^ 2 - 2 a b + b^ 2. Let's use this formula in our case. Here we have the 16 at the beginning and now we start with a squared. So we take the first part and square it which is 8 in our case 8 squared minus 2 * a * b. So 2 * the first part the 8 * the second part the r plus b ^ 2. So in our case r squared then and on the other side we still have the r 2.

[00:04:42]Okay let's simplify a little bit. 8^2 = 64 2 * 8 = 16.

[00:04:55]Um maybe I can calculate this already.

[00:04:58]16 + 64 = 80 in total.

[00:05:05]And now if I take a look at this equation, I have r 2 here and r 2 here.

[00:05:11]So let's subtract r 2 on both sides of the equation. What do I get then? I have my 80 here minus 16 r. This cancels out and on the other side r 2 - r 2 disappears as well and we get a zero.

[00:05:35]Okay. To solve for r, let's bring this to the other side by adding 16 r on both sides of the equation.

[00:05:46]So that I have my 80 here. This disappears on the other side. I have in total 16 R then and to solve for R, we have to get rid of the 16. So let's divide both sides of the equation by this 16 so that it cancels out here and I only have my r and 18 / 16 = 5. We've just found our r. We found our radius of our circle and we solved this problem.

[00:06:24]I'm curious how you solved this problem.

[00:06:26]So, please let me know in the comments.

[00:06:27]I wish you a wonderful day and I hope to see you in one of my next videos. Take care.