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Just angle chasing

Source: III Caucasus Mathematical Olympiad

March 17, 2018
geometry

Problem Statement

Let II be the incenter of an acute-angled triangle ABCABC. Let PP, QQ, RR be points on sides ABAB, BCBC, CACA respectively, such that AP=ARAP=AR, BP=BQBP=BQ and ∠PIQ=∠BAC\angle PIQ = \angle BAC. Prove that QR⊥ACQR \perp AC.
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