Four Concurrent Lines in a Cyclic Quadrilateral

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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.

Drag the purple points to change the figure.


Contributed by: Jay Warendorff (March 2011)
After work by: Alexander Bogomolny
Open content licensed under CC BY-NC-SA



A. Bogomolny, "Four Concurrent Lines in a Cyclic Quadrilateral," Interactive Mathematics Miscellany and Puzzles.

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