Question

A quarter-circle with radius 5 is drawn. A circle is drawn inside the sector, which is tangent to the sides of the sector. Find the radius of the inscribed circle.

Answer 1

I assume the inscribed circle is also tangent to the larger circle.
Draw a diagram. If the inscribed circle has radius r, then
r^2 + r^2 = (5-r)^2
r = 5(√2-1)
To see the result, view

www.wolframalpha.com/input/?i=plot+x%5E2%2By%5E2+%3D+25%2C+%28x-%285%28%E2%88%9A2-1%29%29%29%5E2%2B+%28y-%285%28%E2%88%9A2-1%29%29%29%5E2+%3D+%285%28%E2%88%9A2-1%29%29%5E2%2C+x%3D0%2C+y%3D0