Angle in a semi-circle

The angle in a semi-circle is always a right angle.

Also known as Thales' theorem, after Thales of Miletus (c. 624 BC - c. 546 BC).

This is effectively a special case of angle at the centre is double angle at circumference; the angle at the centre is 180° so the angle at the circumference is half that, ie 90°.

Try moving any of the points and the angle in the semi-circle should always be a right angle.

Notice that the other two angles add to 90° as the three points form a triangle.

To download this Geogebra file click here.