Question 41
Two circles, centres $O_1$ and $O_2$, intersect at $A$ and $B$. Let $O_1C_1$ and $O_2C_2$ be parallel radii of these circles such that $C_1$ and $C_2$ are on the same side of $O_1O_2$. Prove that the circumcircles of triangles $C_1AC_2$ and $C_1BC_2$ have the same radius.