Problem

Source: Romanian National Olympiad 2014, Grade IX, Problem 4

Tags: geometry



Let $ ABCD $ be a quadrilateral inscribed in a circle of diameter $ AC. $ Fix points $ E,F $ of segments $ CD, $ respectively, $ BC $ such that $ AE $ is perpendicular to $ DF $ and $ AF $ is perpendicular to $ BE. $ Show that $ AB=AD. $