Question 175
Given is a quadrangle $ABCD$ whose diagonal $AC$ and $BD$ intersect at point $E$ and whose sides $AD$ and $BC$ lie on straight lines intersecting at $F$ point. The centers of the routes $AB$ and $CD$ are designated $G$ or $H$ respectively. Prove that the straight $EF$ in $E$ touches the circle by $E$, $G$ and $H$.