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BMT 2015 Spring - Geometry P1

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December 30, 2021
geometry

Problem Statement

Suppose that circles C1C_1 and C2C_2 intersect at XX and YY . Let A,BA, B be on C1C_1, C2C_2, respectively, such that A,X,BA, X, B lie on a line in that order. Let A,CA, C be on C1C_1, C2C_2, respectively, such that A,Y,CA, Y, C lie on a line in that order. Let A′,B′,C′A', B', C' be another similarly defined triangle with A≠A′A \ne A'. Prove that BB′=CC′BB' = CC'.
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