A circle lies inside a quarter-circle, as shown below. The circle is tangent to side \(\overline{AO}\) and arc \(AB\) . Find the radius of the circle.
Let the center of the small circle = C
Let the tangent point of the circle with OA = D
Triangle OCD is right such that
OD^2 + DC^2 = OC^2
3^2 + r^2 = (5 - r)^2
9 + r^2 = r^2 - 10r + 25
10r = 16
r = 16 / 10 = 1.6
+70 
