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isosceles, medians cut (ABC) - All-Russian MO 2004 Regional (R4) 9.2

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September 27, 2024
geometryisoscelesMedians

Problem Statement

In triangle ABCABC, medians AA′AA', BB′BB', CC′CC' are extended until they intersect with the circumcircle at points A0A_0, B0B_0, C0C_0, respectively. It is known that the intersection point M of the medians of triangle ABCABC divides the segment AA0AA_0 in half. Prove that the triangle A0B0C0A_0B_0C_0 is isosceles.
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