Question 30
In a trapezoid $ABCD$ with the bases $AD$ and $BC$, a point $F$ is chosen on the side $CD$. Let $E$ be the point of intersection of the lines $AF$ and $BD$. A point $G$ is chosen on the side $AB$ so that $EG \perp AD$. Let $H$ be the point of intersection of the lines $CG$ and $BD$, and let $I$ be the point of intersection of the lines $FH$ and $AB$. Prove that the lines $CI$, $FG$ and $AD$ are concurrent.
