Circle Theorems - Intersecting Radii and Chords

This applet investigates two theorems about Intersecting Radii and Chords.

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 and Intersecting Chords   Parts of Circles  

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How to Use this Applet

The program shows a chord of the circle, AB, intersecting a line from the Centre O at the point M. You can move the points A and B around by clicking and dragging the red circles. There are rules governing this situation, but in effect they are the same rule.

One rule says that if M is the mid-point of AB, then OMA and OMB are right angles (i.e. M is perpendicular to AB). The other says that if OM is perpendicular to AB, then M is the mid-point of AB (i.e. AM = BM). Play around with the program to help you visualise what's going on. Enjoy and learn!