Question 90
Trapezoid $ABCD$, with bases $AB,CD$, is inscribed in a circle $\Omega$. A circle $\omega$ passes through $C,D$ and intersects segments $CA,CB$ at $A_1,B_1$, respectively. Points $A_2,B_2$ are the reflections of $A_1,B_1$ in the midpoints of $CA,CB$, respectively. Prove that $A,B,A_2,B_2$ lie on a circle.
(I. Bogdanov)
(I. Bogdanov)