Question 62
A trapezoid $ABCD$ with the bases $AB$ and $CD$ is inscribed into circle $\Omega$. A circle $\omega$ passes through the points $C$ and $D$, and intersects the segments $CA$ and $CB$ at $A_1 \neq C$ and $B_1 \neq D$, respectively. The points $A_2$ and $B_2$ are symmetric to $A_1$ and $B_1$ with respect to the midpoints of $CA$ and $CB$, respectively. Prove that the points $A, B, A_2$ and $B_2$ are con-cyclic. (I. Bogdanov)