Problem

Source: Stars of Mathematics 2017, Juniors, Problem 4

Tags: geometry



Let $ ABC $ be an acute triangle having $ AB<AC, $ let $ M $ be the midpoint of the segment $ BC, D$ be a point on the segment $ AM, E $ be a point on the segment $ BD $ and $ F $ on the line $ AB $ such that $ EF $ is parallel to $ BC, $ and such that $ AE $ and $ DF $ pass through the orthocenter of $ ABC. $ Prove that the interior bisectors of $ \angle BAC $ and $ \angle BDC, $ together with $ BC $ are concurrent. Vlad Robu