Question 8
Let $I$ be the incenter and $AB$ the shortest side of a triangle $ABC$. The circle with center $I$ and passing through $C$ intersects the ray $AB$ at the point $P$ and the ray $BA$ at the point $Q$. Let $D$ be the point where the excircle of the triangle $ABC$ belonging to angle $A$ touches the side $BC$, and let $E$ be the symmetric of the point $C$ with respect to $D$. Show that the lines $PE$ and $CQ$ are perpendicular.
