Problem

Source:

Tags: geometry, cyclic quadrilateral



Let $ABCD$ be a cyclic quadrilateral. Let $E$ be a point on side $BC,$ $F$ be a point on side $AE,$ $G$ be a point on the exterior angle bisector of $\angle BCD,$ such that $EG=FG,$ $\angle EAG=\dfrac12\angle BAD.$ Prove that $AB\cdot AF=AD\cdot AE.$