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circumcenter lies on circle, BK = AC, CL = AB (Kharkiv City XI 2016 - Ukr)

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March 18, 2020
geometryCircumcentercirclesequal segmentsKharkiv

Problem Statement

The circle ω\omega passes through the vertices BB and CC of triangle ABCABC and intersects its sides AC,ABAC,AB at points A,EA,E, respectively. On the ray BDBD, a point KK such that BK=ACBK = AC is chosen , and on the ray CECE, a point LL such that CL=ABCL = AB is chosen. Prove that the center OO of the circumscribed circle of the triangle AKLAKL lies on the circle ω\omega.
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