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SHARYGIN 2017 Problem 2

    A circle cuts off four right-angled triangles from rectangle ABCD. Let A0,B0,C0A_0, B_0, C_0 and D0D_0 be the midpoints of the correspondent hypotenuses. Prove that A0C0=B0D0A_0C_0 = B_0D_0.

    Official text Sharygin Geometry Olympiad 2017 official paper, page 1. Quoted with source.

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