Three Circles Theorem: Common Chords and Concurrent Point. Level: High School, SAT Prep, College
  

The common chords of three circles A, B, and C taken in pairs are concurrent at the point P.

Click the red button () on the figure to start the animation.
Drag point B to change the figure.
 

Chord is the line segment joining two points on a circle.

Circle is the set of points in a plane that are equidistant from a given point, called center.

Concurrent: Two or more lines are said to be concurrent if they intersect at a single point.

Dynamic Geometry: You can alter the figure above dynamically in order to test and prove (or disproved) conjectures and gain mathematical insight that is less readily available with static drawings by hand.

This page uses the TracenPoche dynamic geometry software and requires Adobe Flash player 7 or higher. TracenPoche is a project of Sesamath, an association of French teachers of mathematics.
 

 

 

 

 

 

 

Three circles theorem

 

 

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Last updated: August 1, 2009