Four Concurrent Lines in a Cyclic Quadrilateral
A cyclic quadrilateral has all four of its vertices on a circle.[more]
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.[less]
A. Bogomolny, "Four Concurrent Lines in a Cyclic Quadrilateral," Interactive Mathematics Miscellany and Puzzles.