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MNPQR , ABCDE similar pentagons, regular?

Source: Romania IMO TST 1991 p9

February 19, 2020
similarpentagongeometryRegular

Problem Statement

The diagonals of a pentagon ABCDEABCDE determine another pentagon MNPQRMNPQR. If MNPQRMNPQR and ABCDEABCDE are similar, must ABCDEABCDE be regular?
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