Given a Chord of a Circle, draw any other two Chords and passing through its Midpoint. Call the points where and meet and . Then is the Midpoint of .
See also Chord, Circle, Midpoint
References
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 45-46, 1967.