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AB+BC=3AC

Source: St. Petersburg MO 2001, 10th grade, P3

April 24, 2023
geometryincenter

Problem Statement

Let II be the incenter of triangle ABCABC and let DD be the midpoint of side ABAB. Prove that if the angle ∠AOD\angle AOD is right, then AB+BC=3ACAB+BC=3AC.
[I]Proposed by S. Ivanov
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