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Reflecting triangle sides across angle bisector

Source: Canada MO 2024/1

March 8, 2024
geometryincentergeometric transformationreflectionangle bisector

Problem Statement

Let ABCABC be a triangle with incenter II. Suppose the reflection of ABAB across CICI and the reflection of ACAC across BIBI intersect at a point XX. Prove that XIXI is perpendicular to BCBC.
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