MathDB

G3

Part of 2020 Balkan MO Shortlist

Problems(1)

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

Source: 2020 Balkan MO shortlist G3

9/14/2021
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
geometrycircumcircleperimeter