Question 191
Two circles $\Gamma_{1}$ and $\Gamma_{2}$ with centers $O_{1}$ and $O_{2}$ meet at $P$ and $Q$. A line through $O_{1}$ meets $\Gamma_{2}$ at $A$ and $B$, and a line through $O_{2}$ meets $\Gamma_{1}$ at $C$ and $D$. Show that if there exists a circle passing through $A, B, C$ and $D$, then the center of this circle lies on $(PQ)$.
