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Internal angle bisector problem

Source: IGO 2022 Elementary P4

December 14, 2022
geometryangle bisectoriranian geometry olympiad

Problem Statement

Let ADAD be the internal angle bisector of triangle ABCABC. The incircles of triangles ABCABC and ACDACD touch each other externally. Prove that ∠ABC>120∘\angle ABC > 120^{\circ}. (Recall that the incircle of a triangle is a circle inside the triangle that is tangent to its three sides.)
Proposed by Volodymyr Brayman (Ukraine)
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