Question 85
Given an inscribed pentagon $ABCDE$ with circumcircle $\Gamma$. Line $\ell$ passes through vertex $A$ and is tangent to $\Gamma$. Points $X, Y$ lie on $\ell$ so that $A$ lies between $X$ and $Y$. Circumcircle of triangle $\triangle XED$ intersects segment $AD$ at $Q$ and circumcircle of triangle $\triangle YBC$ intersects segment $AC$ at $P$. Lines $XE, YB$ intersect at $S$, and lines $XQ, YP$ at $Z$. Prove that circumcircle of triangles $\triangle XYZ$ and $\triangle BES$ are tangent.