Question 82
Heights $BB_1$ and $CC_1$ of acute triangle $ABC$ intersect in point $H$. $B_2$ and $C_2$ are points on segments $BH$ and $CH$ respectively such that $BB_2 = B_1H$ and $CC_2 = C_1H$. Circumcircle of the triangle $B_2HC_2$ intersects circumcircle of triangle $ABC$ in points $D$ and $E$. Prove that triangle $DEH$ is right.