KöMaL 2016 B4765

In a cyclic quadrilateral $ABCD$ , the angle bisectors of angles $ADB\sphericalangle$ and $ACB\sphericalangle$ intersect side $AB$ at points $E$ and $F$ , and the bisectors of $CBD\sphericalangle$ and $CAD\sphericalangle$ intersect side $CD$ at $G$ and $H$ , respectively. Prove that the points $E$ , $F$ , $G$ , $H$ are concyclic.