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the circumcircles of $BCB_1, CAC_1$ and $ABA_1$ are congruent

Source: Moldova TST 1995

August 8, 2023
geometrycircumcircle

Problem Statement

Let ABCABC be a triangle with the medians AA1,BB1AA_1, BB_1 and CC1CC_1{}. Prove that if the circumcircles of BCB1,CAC1BCB_1, CAC_1 and ABA1ABA_1 are congruent then ABCABC is equilateral.
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