Circle Theorems - Angle at the Centre
Maths: Edexcel A Level Pure Maths, topic 3.2.5
Circle Theorems
Angle at centre is double the angle at the circumference
Proof
- Split the shape into two isosceles triangles and label the angles.
- The angle at the centre is 360° - x - y and the angle at the circumference is a + b.
Proof continued
- Since the angles in a triangle add up to 180°:
a = 1⁄2(180° - y), b = 1⁄2(180° - x) - So angle at circumference = a + b = 1⁄2(360° - x - y)
= 1⁄2 × angle at centre.
Test yourself on Circle Theorems - Angle at the Centre
What is the value of angle x?
What is the value of angle x?
What is the value of angle x?
What is the value of angle x?