Second circle theorem

First page
Theorem 1
Theorem 2
Theorem 3
Theorem 4
Theorem 5
Theorem 6
Theorem 7
The Seven Theorems

Angle in a semicircle

Second circle theorem:

What's the size of the angle α ('angle in a semicircle')?

You can use the cursor to move point D around the circumference;
It doesn't change angle α though!!
It is always 90 degrees.
This theorem is a special case of theorem 1 - 'angle at the centre is twice the angle at the circumference', with the centre angle = 180 degrees.

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to If you need them, the seven circle theorems here

Tim Devereux, Created with GeoGebra