Circle Theorems - Chords

# Circle Theorems - Chords

GCSE(H),

A line drawn from the centre of a circle to bisect a chord will be perpendicular to the chord.

## Examples

1. A circle of radius 10cm has a chord drawn across it of length 12cm. What is the distance from the midpoint of the chord to the centre of the circle?

The distance from the midpoint of the chord to the circumference is 6cm. This forms a right angled triangle with the radius. Using Pythagoras:

10^2 = 6^2 + x^2

100 - 36 = x^2

x^2 = 64

x = 6

2. What is the size of the angle ∠AOB?