Question 65
Triangle $ABC$ is inscribed in a circle $\Gamma$. The points $X, Y$ and $Z$ are the midpoints of those arcs $BC, CA$ and $AB$, respectively, on $\Gamma$ which do not contain the third point of the triangle. The intersection of the triangles $ABC$ and $XYZ$ form a hexagon $DEFGHK$. Prove that the diagonals $DG, EH$ and $FK$ are concurrent.