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Prove that the circumcentre appears on a circumcircle

Source: Lusophon Mathematical Olympiad 2024 Day 1 Problem 3

July 26, 2024
geometrycircumcircleincenter

Problem Statement

Let ABCABC be a triangle with incentre II. A line rr that passes through II intersects the circumcircles of triangles AIBAIB and AICAIC at points PP and QQ, respectively. Prove that the circumcentre of triangle APQAPQ is on the circumcircle of ABCABC.
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