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Isosceles triangles

Source: Brazilian Math Olympiad 2006, Problem 1

October 30, 2006
geometryincenterangle bisectorgeometry unsolved

Problem Statement

Let ABCABC be a triangle. The internal bisector of ∠B\angle B meets ACAC in PP and II is the incenter of ABCABC. Prove that if AP+AB=CBAP+AB = CB, then APIAPI is an isosceles triangle.
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