Question 34
The incircle of the triangle $ABC$ has center $I$ and touches $BC$, $CA$, $AB$ at $D$, $E$, $F$ respectively. The segments $AI$, $BI$, $CI$ intersect the circle at $D'$, $E'$, $F'$ respectively. Show that $DD'$, $EE'$, $FF'$ are collinear.