Let ABC be a triangle and let Γ be its circumcircle. Let D be a point on AB such that CD is parallel to the line tangent to Γ at A. Let E be the intersection of CD with Γ distinct from C, and F the intersection of BC with the circumcircle of △ADC distinct from C. Finally, let G be the intersection of the line AB and the internal bisector of ∠DCF. Show that E, G, F and C lie on the same circle. geometrycircumcirclecyclic quadrilateral