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Quadrilateral with two equal angles, perpendicularity wanted

Source: 2021 Oral Moscow Geometry Olympiad grades 8-9 p3

May 17, 2021
geometryperpendicular lines

Problem Statement

ABCDABCD is a convex quadrilateral such that ∠A=∠C<90∘\angle A = \angle C < 90^{\circ} and ∠ABD=90∘\angle ABD = 90^{\circ}. MM is the midpoint of ACAC. Prove that MBMB is perpendicular to CDCD.
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