Four Concurrent Lines in a Cyclic Quadrilateral

A cyclic quadrilateral has all four of its vertices on a circle.
Through the midpoint of each side of a cyclic quadrilateral draw a line perpendicular to the opposite side or its extension. The four resulting lines are concurrent.
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A. Bogomolny, "Four Concurrent Lines in a Cyclic Quadrilateral," Interactive Mathematics Miscellany and Puzzles.
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