MathNet 2018-part-01 — 181 problems (EN–VI) Question 121

Let $ABCD$ be a cyclic quadrilateral with the circumcircle $\omega$. The points $B_1$ and $D_1$ are symmetric to $A$ with respect to the midpoints of $BC$ and $CD$ respectively. The circumcircle of the triangle $CB_1D_1$ intersects $\omega$ at $C$ and $G$.
Prove that $AG$ is a diameter of $\omega$.
(A. Voidelevich)