Geometry · SS 2
Angle at the centre of a circle
Find angles inside a circle standing on the same arc.
- Angle at centre = 2 × angle at circumference
- Angles in the same segment are equal · Angle in a semicircle = 90°
What the letters mean
- centre angle
- the angle at O, the centre, made by the arc
- circumference angle
- the angle on the edge of the circle made by the same arc
Worked example
An angle at the circumference is 35°. Find the angle at the centre on the same arc.
Step 1: Double it
2 × 35° = 70°
Final answer: 70°
See it
Play with this picture from the Angles in a Circle lesson.
∠AOB = 120° = 2 × ∠ACB = 60°