Circle inscribed in semi-circle.

Problem solving using the Pythagorean Theorem. Challenge problem.
Point A lies on the diameter of a semi–circle with the radius 8 cm and the center O. Another circle is inscribed in the semi–circle so that it touches the diameter at point A and also touches the circumference of the semi– circle. Given OA = 4, find the radius of the inscribed circle. Express your answer in cm.