SHARYGIN 2017 Problem 14

Let points $B$ and $C$ lie on the circle with diameter $AD$ and center $O$ on the same side of $AD$ . The circumcircles of triangles $ABO$ and $CDO$ meet $BC$ at points $F$ and $E$ respectively. Prove that $R^2 = AF.DE$ , where $R$ is the radius of the given circle. Proposed by N.Moskvitin