Let A, B and C be points lying on a circle Γ with centre O. Assume that ∠ABC>90. Let D be the point of intersection of the line AB with the line perpendicular to AC at C. Let l be the line through D which is perpendicular to AO. Let E be the point of intersection of l with the line AC, and let F be the point of intersection of Γ with l that lies between D and E.
Prove that the circumcircles of triangles BFE and CFD are tangent at F. geometrycircumcirclereflectionBMO