Question 62
In $\triangle ABC$, point $B_2$ is the reflection of the center of B-excircle with respect to the midpoint of side $AC$, and point $C_2$ is the reflection of the center of C-excircle with respect to the midpoint of side $AB$. The A-excircle touches side $BC$ at point $D$. Prove that $AD \perp B_2C_2$. (posed by Bian Hongping)