Question 19
Circles $k_1$ and $k_2$ intersect in points $A$ and $B$. Line $l$ intersects circle $k_1$ in points $C$ and $E$, and circle $k_2$ in points $D$ and $F$ in such a way that $D$ is between $C$ and $E$, and $E$ is between $D$ and $F$. Lines $CA$ and $BF$ intersect in point $G$, and lines $DA$ and $BE$ in point $H$.
Prove that $CF \parallel HG$.
Prove that $CF \parallel HG$.