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angle wanted, 3 angles and 3 circles related 1999 HMMT Team 11

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January 1, 2022
HMMTgeometrycirclesangles

Problem Statement

Circles C1C_1, C2C_2, C3C_3 have radius 1 1 and centers O,P,QO, P, Q respectively. C1C_1 and C2C_2 intersect at AA, C2C_2 and C3C_3 intersect at BB, C3C_3 and C1C_1 intersect at CC, in such a way that ∠APB=60o\angle APB = 60^o , ∠BQC=36o\angle BQC = 36^o , and ∠COA=72o\angle COA = 72^o . Find angle ∠ABC\angle ABC (degrees).
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