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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

Butterfly theorem proof

 

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.

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