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angle chasing, OI line (V Soros Olympiad 1998-99 Round 2 10.6)

Source:

May 25, 2024
geometryangles

Problem Statement

The straight line containing the centers of the circumscribed and inscribed circles of triangle ABCABC intersects rays BABA and BCBC and forms an angle with the altitude to side BCBC equal to half the angle ∠BAC\angle BAC. What is angle ∠ABC\angle ABC?
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