Circle Theorems - Intersecting Chords and Secants

This applet investigates the Intersecting Chords Theorem and the Intersecting Secants theorem.

Author and programmer: Ron Barrow

UK Years 10-11, Ages 14-16, KS4, iGCSE Mathematics - Geometry, Shape and Space

   
           

Instructions below   Waldomaths video  See also:    2 Circle Theorems   2 More Circle Theorems   Alternate Segment Theorem   Circles and Tangents   Circles and Isosceles Triangles   Circles - Radii and Chords   Parts of Circles  

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How to Use this Applet

The program shows two chords of the circle - AC and BD - which intersect at the point M. You can move the points A, B, C and D around by clicking and dragging the red circles. There is a rules governing the way M divides the two chords. It is called the Intersecting Chords Theorem, and says that MA×MC = MB×MD.

If you drag two points past each other, the point M then moves outside the circle, but the relationship MA×MC = MB×MD is still true. In this situation it is known as the Intersecting Secants Theorem (a secant is a chord which extends outside the circle), or sometimes as the Intersecting Chords Theorem Extended.

Both theorems are important and useful.