Question 155
Given the triangle $ABC$, let $k$ be the excircle at the side $BC$. Choose any line $p$ parallel to $BC$ intersecting line segments $AB$ and $AC$ at points $D$ and $E$. Denote by $l$ the incircle of the triangle $ADE$. The tangents from $D$ and $E$ to the circle $k$ not passing through $A$ intersect at $P$. The tangents from $B$ and $C$ to the circle $l$ not passing through $A$ intersect at $Q$. Prove that the line $PQ$ passes through a fixed point independent of the choice of $p$.