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cyclic wanted, <QAC=<ABC,<PAB=<ACB Puerto Rico Ibero IMO TST 2018.2

Source:

September 16, 2021
geometrycyclic quadrilateralequal anglesConcyclic

Problem Statement

Let ABCABC be an acute triangle and let P,QP,Q be points on BCBC such that ∠QAC=∠ABC\angle QAC =\angle ABC and ∠PAB=∠ACB\angle PAB = \angle ACB. We extend APAP to MM so that P P is the midpoint of AMAM and we extend AQAQ to NN so that QQ is the midpoint of ANAN. If T is the intersection point of BMBM and CNCN, show that quadrilateral ABTCABTC is cyclic.
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