Question 9
Triangle $ABC$ has $\angle BAC=90^\circ$. Let $D$ be the foot of the altitude from $A$ to $BC$, and let $I_1,I_2$ be the incenters of triangles $ABD,ACD$, respectively. Let $M,K$ be the perpendicular feet from $I_1,I_2$ to segment $AD$, respectively. If $I_1M+I_2K=BC/4$, find the angles of triangle $ABC$.
