Problem

Source: Iran MO 3rd round 2019 finals - Geometry P3

Tags: geometry



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 $XED$ intersects segment $AD$ at $Q$ and circumcircle of triangle $YBC$ intersects segment $AC$ at $P$. Lines $XE,YB$ intersects each other at $S$ and lines $XQ, Y P$ at $Z$. Prove that circumcircle of triangles $XY Z$ and $BES$ are tangent.