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MMO 229 Moscow MO 1952 angle chasing in a triangle 80-80-20

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August 8, 2019
geometryisoscelesangleAngle Chasing

Problem Statement

In an isosceles triangle △ABC,∠ABC=20o\vartriangle ABC, \angle ABC = 20^o and BC=ABBC = AB. Points PP and QQ are chosen on sides BCBC and ABAB, respectively, so that ∠PAC=50o\angle PAC = 50^o and ∠QCA=60o\angle QCA = 60^o . Prove that ∠PQC=30o\angle PQC = 30^o .
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