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Line through intersection of diagonals of cyclic quad and mipoint of side

Source: 2019 Pan-African Shortlist - G3

January 18, 2021
geometrycyclic quadrilateral

Problem Statement

Let ABCDABCD be a cyclic quadrilateral with its diagonals intersecting at EE. Let MM be the midpoint of ABAB. Suppose that MEME is perpendicular to CDCD. Show that either ACAC is perpendicular to BDBD, or ABAB is parallel to CDCD.
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