The circle theorems

4) Angles in a semicircle

The angle at the circumference in a semicircle is a right angle.

Triangle (ABP) within circle, passing through centre, O

Angle APB = 90°


Example

Calculate the angle z.

Triangle (STU) within circle, passing through centre, O

The angle at the circumference in a semi-circle is 90°.
Angle STU = 90°
Angles in a triangle add up to 180°.

z = 180° – 90° – 31° = 59°


Proof

The angle on a straight line is 180°. The angle VOY = 180°.

Triangle (VWY) within circle, passing through centre, O

The angle at the centre is double the angle at the circumference.

Angle VWY = 1/2 of angle VOY = 1/2 x 180°.
Angle VWY = 90°


< Previous | 1 | 2 | 3 | 4 | 5 | 6 | 7 | Next >>