Question 52
The incircle of a triangle $ABC$ touches the three sides $BC$, $CA$ and $AB$ at $D$, $E$ and $F$ respectively. The line segments $BE$ and $CF$ intersect the incircle at $Y$ and $Z$ respectively. Suppose the lines $FE$ and $BC$ intersect externally at $X$. Prove that the three points $X$, $Y$ and $Z$ are collinear.