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symmetrics of circumcenter wrt sides create a congruent triangle

Source: 2018 Portugal p4

October 11, 2020
geometrycircumcircleSymmetriccongruent triangles

Problem Statement

Let [ABC][ABC] be any triangle and let D,ED, E and FF be the symmetrics of the circumcenter wrt the three sides. Prove that the triangles [ABC][ABC] and [DEF][DEF] are congruent. https://cdn.artofproblemsolving.com/attachments/c/6/45bd929dfff87fb8deb09eddb59ef46e0dc0f4.png
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