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Sharygin CR 2019 P1

Source:

March 6, 2019
geometry

Problem Statement

Let AA1AA_1, CC1CC_1 be the altitudes of ΔABC\Delta ABC, and PP be an arbitrary point of side BCBC. Point QQ on the line ABAB is such that QP=PC1QP = PC_1, and point RR on the line ACAC is such that RP=CPRP = CP. Prove that QA1RAQA_1RA is a cyclic quadrilateral.
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