IMO 1985 LL SPA73

Let A1A2, B1B2, C1C2 be three equal segments on the three

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IMO 1985 LL SPA73

Origin: SPA

Problem

Let A1A2, B1B2, C1C2 be three equal segments on the three sides of an equilateral triangle. Prove that in the triangle formed by the lines B2C1, C2A1, A2B1, the segments B2C1, C2A1, A2B1 are proportional to the sides in which they are contained.