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Concyclic points

Source: IZHO 2017 day 1 p1

January 14, 2017
geometry

Problem Statement

Let ABCABC be a non-isosceles triangle with circumcircle ω\omega and let H,MH, M be orthocenter and midpoint of ABAB respectively. Let P,QP,Q be points on the arc ABAB of ω\omega not containing CC such that ∠ACP=∠BCQ<∠ACQ\angle ACP=\angle BCQ < \angle ACQ.Let R,SR,S be the foot of altitudes from HH to CQ,CPCQ,CP respectively. Prove that thé points P,Q,R,SP,Q,R,S are concyclic and MM is the center of this circle.
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