Let ABC be an acute triangle such that AC<BC and ω its circumcircle. M is the midpoint of BC. Points F and E are chosen in AB and BC, respectively, such that AC=CF and EB=EF. The line AM intersects ω in D=A. The line DE intersects the line FM in G. Prove that G lies on ω. geometrycircumcirclebutterfly theoremcono surlines meeting at circmucirclegeometry solved