Question 81
Circles $\Gamma_1$ and $\Gamma_2$ meet at points $X$ and $Y$. A circle $S_1$ touches $\Gamma_1$ internally at $A$ and $\Gamma_2$ externally at $B$. A circle $S_2$ touches $\Gamma_2$ internally at $C$ and $\Gamma_1$ externally at $D$.
Prove that the points $A$, $B$, $C$, $D$ are either collinear or concyclic.
Prove that the points $A$, $B$, $C$, $D$ are either collinear or concyclic.