Question 78
Given a triangle $A B C$, a circle $k$ is tangent to the lines $A B$ and $A C$ at $B$ and $P$. Let $H$ be the foot of perpendicular from the center $O$ of $k$ to $B C$, and let $T$ be the intersection point of $O H$ and $B P$. Prove that $A T$ bisects the segment $B C$.