Question 78
Let $ABCD$ be a quadrilateral inscribed in a circle $\Gamma$. Let $E$, $F$, $G$, $H$ be the midpoints of the arcs $AB$, $BC$, $CD$, $DA$ of the circle $\Gamma$. Suppose $AC \cdot BD = EG \cdot FH$. Prove that $AC$, $BD$, $EG$, $FH$ are concurrent.