OME 2009 Problem 2

Let $ABC$ be an acute triangle with the incircle $C(I,r)$ and the circumcircle $C(O,R)$ . Denote $D\in BC$ for which $AD\perp BC$ and $AD = h_a$ . Prove that $DI^2 = (2R - h_a)(h_a - 2r)$ .