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tangent to the circumcircle when tangent to a given point and a line

Source: INAMO Shortlist 2014 G6

July 13, 2019
geometrycircumcircletangent circlestangent

Problem Statement

Given an ABCABC acute triangle with OO the center of the circumscribed circle. Suppose that ω\omega is a circle that is tangent to the line AOAO at point AA and also tangent to the line BCBC. Prove that ω\omega is also tangent to the circumcircle of the triangle BOCBOC.
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