Circle Theorems 3 - The Alternate Segment Theorem

This applet investigates the Alternate Segment Theorem

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

Instructions below   light background   Waldomaths video  See also: Circle Theorems: 1  2  4  Triangles  Circle Parts

[Applet - Circle theorems 3]

The line PQ is a tangent to the circle, touching the circle only once at the point A.
You can move the points A, B and C around by clicking them and dragging them with your mouse. As you do so, look carefully at the size of the angles. There are different colours to help you.

The sizes of the angles follow an important rule (theorem), which you can see by clicking "Show Theorem" at the bottom. Try not to do this - try to work the rule out by yourself! Enjoy yourself while you practise and learn this theorem by name.