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Two circles intersect on circumcircle

Source: IV Caucasus Mathematic Olympiad

April 7, 2019
geometrycircumcircle

Problem Statement

In a triangle ABCABC let II be the incenter. Prove that the circle passing through AA and touching BIBI at II, and the circle passing through BB and touching AIAI at II, intersect at a point on the circumcircle of ABCABC.
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