Question

Let ABCD be a square with side length 100. A circle with center C and radius CD is drawn. Another circle of radius r lying inside ABCD, is drawn to touch this circle externally and such that the circle also touches AB and AD. If r= m + $\sqrt{k}$ , where m and n are integers and k is the prime number, find the value of $\frac{m+n}{k}$ .

Answer 1

Answer:

Let ABCD be a square with side length 100. A circle with center C and radius CD is drawn. Another circle of radius r lying inside ABCD, is drawn to touch this circle externally and such that the circle also touches AB and AD. If r= m + $\sqrt{k}$ , where m and n are integers and k is the prime number, find the value of $\frac{m+n}{k}$ .