Given an isosceles triangle ABC with base BC. Inside the side BC is given a point D. Let E,F be respectively points on the sides AB,AC that ∣∠BED∣=∣∠DFC∣>90o . Prove that the circles circumscribed around the triangles ABF and AEC intersect on the line AD at a point different from point A. (Patrik Bak, Michal Rolínek) geometryconcurrentequal anglesisoscelesconcurrency