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Four circles and quadrilateral

Source: BdMO 18

February 27, 2019
geometry

Problem Statement

Four circles are drawn with the sides of quadrilateral ABCDABCD as diameters. The two circles passing through AA meet again at EE . The two circles passing through BB meet again at FF . The two circles passing through CC meet again at GG. The two circles passing through DD meet again at HH. Suppose, E,F,G,H E, F, G,H are all distinct. Is the quadrilateral EFGHEFGH similar to ABCDABCD ? Show with proof.
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