Butterfly Theorem Proof: Circle, Chord, Midpoint,
Inscribed Angle, SAS Similarity, Cyclic Quadrilateral,
ASA Congruence. Level: High School, College.
Step-by-step illustration. Online Geometry Problem 804

The figure above shows a circle O and a chord AB with midpoint C. The chords DE and FG passing through C intersect AB at M and N, respectively. Prove that C is the midpoint of MN.
See also:
Butterfly Theorem: HTML5 version.