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Angle between points of intersections of angular bisectors with opposite sides

Source: Bundeswettbewerb Mathematik 2021, Round 1 - Problem 3

April 12, 2021
geometrygeometry proposed

Problem Statement

Consider a triangle ABCABC with ∠ACB=120∘\angle ACB=120^\circ. Let A’,B’,C’A’, B’, C’ be the points of intersection of the angular bisector through AA, BB and CC with the opposite side, respectively. Determine ∠A’C’B’\angle A’C’B’.
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