Can you find the Value of R?

In this figure, a circle center O is divided into four quadrants. If this length is 17 units and this length is 7 units, find the radius of the circle. To solve this problem, first let's label this point A, B, and C. Let the radius of the circle Next, let's focus on triangle ABO. Triangle ABO is a right triangle. From Pythagoras' theorem, Substituting these values in the formula, 17 squared is equal to x squared plus y squared. If we make y squared the subject of the formula, we will have y squared is equal to 17 squared minus x squared. Let's call this equation 1. Next, let's draw a straight line from O to C. Observe that OC is also the radius of the circle. Now, let's focus on triangle OBC. Triangle OBC is also a right triangle. So, from Pythagoras' theorem, If we plug in these values in the equation, we will have But from equation 1, So, if we substitute y squared with 17 squared minus x squared, we will have x squared is equal to 7 squared plus 17 squared minus x squared. Taking minus x squared to the left side will give us x squared plus x squared is equal to 7 squared plus 17 squared. x squared plus x squared is 2x squared. 7 squared is 49 and 17 squared is 289. 49 plus 289 is equal to 338. So, 2x squared is equal to 338. Next, let's divide through by 2. 2 will cancel out 2 and we are left with x squared. 338 divided by 2 is 169. So, we are left with x squared is equal to 169. Taking the square root of both sides will give us x is equal to 13 units. And this is the radius of the circle. Thanks for watching.