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Source: Sharygin Correspondence Round 2024 P12

March 6, 2024
geometry

Problem Statement

The bisectors AA1,CC1AA_1, CC_1 of a triangle ABCABC with ∠B=60∘\angle B = 60^{\circ} meet at point II. The circumcircles of triangles ABC,A1IC1ABC, A_1IC_1 meet at point PP. Prove that the line PIPI bisects the side ACAC.
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