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Diagonals of quadriateral are equal

Source: Sharygin Geometry Olympiad Correspondence Round 2017 P-2(Grade-8)

May 1, 2017
geometry

Problem Statement

A circle cuts off four right-angled triangles from rectangle ABCDABCD.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 Proosed by L.Shteingarts
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