The dynamic geometry figure below shows a circle O with M midpoint of a chord AB. Chords CD and EF pass through M. Chords CF and DE intersect AB at G and H, respectively. Prove that M is the midpoint of GH.

Interactive step-by-step animation using GeoGebra

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GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students. Many parts of GeoGebra have been ported to HTML5.

Geometry Problems

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Ten problems: 1411-1420

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Triangle

Circle

Chord

Midpoint

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