Question 100
In a triangle $\triangle ABC$ let the incircle be tangent to $BC$, $CA$, $AB$ at $D$, $E$, $F$, respectively, and let the excircle opposite to $A$ be tangent to $BC$, $CA$, $AB$ at $P$, $Q$, $R$, respectively. Let $EX$ and $FY$ be altitudes in triangle $\triangle DEF$, and $QZ$ and $RW$ altitudes in triangle $\triangle PQR$. Prove that the points $X$, $Y$, $Z$, $W$ are collinear.