CWMO 2013 Problem 3

Let $ABC$ be a triangle, and $B_1,C_1$ be its excenters opposite $B,C$ . $B_2,C_2$ are reflections of $B_1,C_1$ across midpoints of $AC,AB$ . Let $D$ be the extouch at $BC$ . Show that $AD$ is perpendicular to $B_2C_2$