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AQ=BP if AP=PQ=QC, <PBQ = 30^o, equilateral (2021 Novosibirsk Oral Geo Oly 7.6)

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April 27, 2021
geometryequal segmentsEquilateral

Problem Statement

Inside the equilateral triangle ABCABC, points PP and QQ are chosen so that the quadrilateral APQCAPQC is convex, AP=PQ=QCAP = PQ = QC and ∠PBQ=30o\angle PBQ = 30^o. Prove that AQ=BPAQ = BP.
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