Question 15
G3 (RUS) A circle $\omega$ is tangent to two parallel lines $l_1$ and $l_2$. A second circle $\omega_1$ is tangent to $l_1$ at $A$ and to $\omega$ externally at $C$. A third circle $\omega_2$ is tangent to $l_2$ at $B$, to $\omega$ externally at $D$, and to $\omega_1$ externally at $E$. $AD$ intersects $BC$ at $Q$. Prove that $Q$ is the circumcenter of triangle $CDE$.