Question 6
Diagonals of a convex quadrilateral $ABCD$ intersect at $E$. The four points of tangency of the circles $(ABE)$ and $(CDE)$ with their external common tangents lie on a circle $\omega$. Analogously, the four points of tangency of the circles $(ADE)$ and $(BCE)$ with their external common tangents lie on a circle $\gamma$. Prove that the centers of $\omega$ and $\gamma$ coincide.
*(A. D. Tereshin)*
*(A. D. Tereshin)*