Question 60
Let $ABCD$ be a cyclic quadrilateral and let $E$ be the point of intersection of its diagonals $AC$ and $BD$. Suppose $AD$ and $BC$ meet in $F$. Let the midpoints of $AB$ and $CD$ be $G$ and $H$ respectively. If $\Gamma$ is the circumcircle of triangle $EGH$, prove that $FE$ is tangent to $\Gamma$.