Question 71
Let $ABCD$ be a rectangle, $GH \parallel BC$, with $G \in (AB)$ and $H \in (DC)$, and $EF \parallel DC$, with $E \in (AD)$ and $F \in (BC)$. Let $GH \cap EF = \{M\}$ and $AH \cap CE = \{K\}$. Prove that the point $K$ is on the circle passing through the feet of the altitudes of the triangle $DFG$.