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circumcenter lies on perimeter of ABC, squares on sides of triangle

Source: 2020 Balkan MO shortlist G3

September 14, 2021
geometrycircumcircleperimeter

Problem Statement

Let ABCABC be a triangle. On the sides BCBC, CACA, ABAB of the triangle, construct outwardly three squares with centres OaO_a, ObO_b, OcO_c respectively. Let ω\omega be the circumcircle of △OaObOc\vartriangle O_aO_bO_c. Given that AA lies on ω\omega, prove that the centre of ω\omega lies on the perimeter of △ABC\vartriangle ABC.
Sam Bealing, United Kingdom
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