Question 76
Let $\omega$ and $I$ be the incircle and the incentre of a triangle $ABC$, respectively. Let $E$ and $F$ be the tangency points of $\omega$ with the sides $AC$ and $AB$, respectively. The perpendicular bisector of $AI$ intersects $AC$ at a point $P$. Point $Q$ lies on $AB$ and satisfies $QI \perp FP$. Prove that $EQ \perp AB$.