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centroids coincide, right triangles on side of a triangle externally

Source: 2010 XIII All-Ukrainian Tournament of Young Mathematicians, Qualifying p15

May 19, 2021
geometryCentroidright triangleUkrainian TYM

Problem Statement

On the sides of the triangle ABCABC externally constructed right triangles ABC1ABC_1, BCA1BCA_1, CAB1CAB_1. Prove that the points of intersection of the medians of the triangles ABCABC and A1B1C1A_1B_1C_1 coincide.
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