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BP bisects AC, incircle (2022 Adygea Teachers' Geometry Olympiad p3)

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February 28, 2024
geometrybisects segmentincircle

Problem Statement

The incircle of triangle ABCABC touches its sides at points A′A', B′B', C′C'. II is its center. Straight line B′IB'I intersects segment A′C′A'C' at point PP. Prove that straight line BPBP passes through the midpoint of ACAC.
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