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2017 Polish Junior Math Olympiad First Round P2

Source: 2017 Polish Junior Math Olympiad First Round

May 23, 2023
geometry

Problem Statement

Consider an acute triangle ABCABC with ∠ACB=45∘ .\angle ACB=45^\circ\,. Let BCEDBCED and ACFGACFG be squares lying outside triangle ABCABC. Prove that the midpoint of segment DGDG coincides with the circumcenter of triangle ABCABC.
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