# 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

TweetInstructions below 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

## 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!