Question 20
G1 (NET). In the plane we are given two circles intersecting at $X$ and $Y$. Prove that there exist four points $A,B,C,D$ with the following property: For every circle touching the two given circles at $A$ and $B$, and meeting the line $XY$ at $C$ and $D$, each of the lines $AC,AD,BC,BD$ passes through one of these points.