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ILL 1971 Problem 24

    Let A,B,A, B, and CC denote the angles of a triangle. If sin⁡2A+sin⁡2B+sin⁡2C=2\sin^2 A + \sin^2 B + \sin^2 C = 2 , prove that the triangle is right-angled.

    Dataset text AI-MO AoPS. Quoted with source.

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