Question 44
Let $ABCD$ be a square and let $E$ and $F$ be two points outside the square, such that $BEC$ and $CFD$ are equilateral triangles. Let $G$ be the intersection of the lines $BE$ and $FD$, and let $H$ be a point, such that the quadrilateral $CEHF$ is a rhombus. Prove that the points $G$, $E$, $H$ and $F$ lie on the same circle.