Given an acute triangle ABC with AB<AC. Points P and Q lie on the angle bisector of ∠BAC so that BP and CQ are perpendicular on that angle bisector. Suppose that point E,F lie respectively at sides AB and AC respectively, in such a way that AEPF is a kite. Prove that the lines BC,PF, and QE intersect at one point. geometryangle bisectorconcurrencyconcurrent