Circle Theorems 6 - Isosceles Triangles

This applet investigates isosceles triangles drawn inside circles.

Author and programmer: Ron Barrow

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

Instructions below    See also:    2 Circle Theorems   2 More Circle Theorems   Alternate Segment Theorem   Circles and Tangents   Parts of Circles

How to Use this Applet

O is the centre of the circle and A and B are points on its circumference. The triangle OAB has two lines that are equal in length, OA and OB, since both are radii of the circle. The triangle OAB is therefore isosceles. By ticking "Show point C" you draw a new point C on the circle, and now there are three isosceles triangles. The three points can be moved with the mouse and also you can hightlight the three triangles in turn by clicking the radio buttons at the bottom.
The idea is important in understanding angles in triangles, and several important rules or theorems depend on isosceles triangles.