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line passes through arc midpoint

Source: IV Soros Olympiad 1997-98 R3 10.2 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 2, 2024
geometryarc midpoint

Problem Statement

Let MM be the point of intersection of the diagonals of the inscribed quadrilateral ABCDABCD. Prove that if AB=AM,AB = AM, then a line passing through MM perpendicular to ADAD passes through the midpoint of the arc BCBC.
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