Triangle ABC is inscribed in circle ω with AB=5, BC=7, and AC=3. The bisector of angle A meets side BC at D and circle ω at a second point E. Let γ be the circle with diameter DE. Circles ω and γ meet at E and a second point F. Then AF2=nm, where m and n are relatively prime positive integers. Find m+n. trigonometryanalytic geometrygeometrycircumcirclegeometric transformationreflectionratio