Question 82
In triangle $ABC$, whose longest side is $BC$, the angle bisectors meet at $I$. The lines $AI,BI,CI$ meet $BC,CA,AB$ at $D,E,F$, respectively. Points $G$ and $H$ lie on segments $BD$ and $CD$, respectively, and satisfy $\angle GID=\angle ABC$ and $\angle HID=\angle ACB$. Prove that $\angle BHE=\angle CGF$.