A line drawn from the centre of a circle to bisect a chord will be perpendicular to the chord.
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?
Answer: 6 cm
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?
∠AOM = 180 - 90 - 49 = 41º
∠AOB is twice the size of ∠AOM = 2 x 41 = 82º