Dynamic Geometry 1474: Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration

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.

See solution below

Static Diagram of Geometry Problem 1474

Problem 1474 Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration, iPad Apps

Poster of the Butterfly Theorem 1474 using iPad Apps

Dynamic Geometry  1474: Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration Using GeoGebra, iPad Apps

Search gogeometry.com

Classroom Resource:
Interactive step-by-step animation using GeoGebra

This step-by-step interactive illustration was created with GeoGebra.

  • To explore (show / hide): click/tap a check box.
  • To stop/play the animation: click/tap the icon in the lower left corner.
  • To go to first step: click/tap the "Go to step 1" button.
  • To manipulate the interactive figure: click/tap and drag the blue points or figures.

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.

Recent Additions

Geometry Problems
Open Problems
Visual Index
Ten problems: 1411-1420
All Problems
Classical Theorems
HTML5 and Dynamic Geometry
iPad Apps
View or Post a solution

Geometry Problem 1474 Solution(s)