Problem

Source: Indonesian TST Stage 1: Test 4 - Geometry

Tags: geometry, circumcircle, concurrency



Given an acute triangle ABC with altitudes AD and BE intersecting at H, M is the midpoint of AB. A nine-point circle of ABC intersects with a circumcircle of ABH on P and Q where P lays on the same side of A (with respect to CH). Prove that ED,PH,MQ are concurrent on circumcircle ABC