Point $P$ lies on the median from vertex $C$ of a triangle $ABC$. Line $AP$ meets $BC$ at $X$, and line $BP$ meets $AC$ at $Y$ . Prove that if quadrilateral $ABXY$ is cyclic, then triangle $ABC$ is isosceles.
Source: Czech-Polish-Slovak 2003 Q4
Tags: geometry unsolved, geometry
Point $P$ lies on the median from vertex $C$ of a triangle $ABC$. Line $AP$ meets $BC$ at $X$, and line $BP$ meets $AC$ at $Y$ . Prove that if quadrilateral $ABXY$ is cyclic, then triangle $ABC$ is isosceles.