IMO 1971 LL HUN25

Let ABC, AA1A2, BB1B2, CC1C2 be four equilateral triangles

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IMO 1971 LL HUN25

Origin: HUN

Problem

Let ABC, AA1A2, BB1B2, CC1C2 be four equilateral triangles in the plane satisfying only that they are all positively oriented (i.e., in the counterclockwise direction). Denote the midpoints of the segments A2B1, B2C1, C2A1 by P, Q, R in this order. Prove that the triangle PQR is equilateral.