Question 33
Let $ABC$ be a triangle. Its incircle meets the sides $BC$, $CA$ and $AB$ in the points $D$, $E$ and $F$, respectively. Let $P$ denote the intersection point of $ED$ and the line perpendicular to $EF$ and passing through $F$, and similarly let $Q$ denote the intersection point of $EF$ and the line perpendicular to $ED$ and passing through $D$.
Prove that $B$ is the mid-point of the segment $PQ$.
Prove that $B$ is the mid-point of the segment $PQ$.