Question 58
Let $ABC$ be an acute triangle, $I$ the incenter of triangle $ABC$, $r$ its inradius and $R$ the circumradius of triangle $ABC$. Draw the altitude $AD = h_{a}$, with $D$ on side $BC$. Prove that
$$
DI^{2} = (2R - h_{a})(h_{a} - 2r)
$$
$$
DI^{2} = (2R - h_{a})(h_{a} - 2r)
$$