let ABCD be a cyclic quadrilateral with E,an interior point such that AB=AD=AE=BC. Let DE meet the circumcircle of BEC again at F. Suppose a common tangent to the circumcircle of BEC and DEC touch the circles at F and G respectively. Show that GE is the external angle bisector of angle BEF geometrycyclic quadrilateralcircumcircleangle bisector