A circle has a radius of 15 cm. A chord is drawn. The distance from the centre of the circle to the chord is 9 cm. What is the length of the chord?

Step-by-step solution

Idea: Chord length = 2√(r² − d²): the perpendicular from the centre bisects the chord and forms a right triangle with the radius.

1. OM ⟂ AB, so M is the midpoint of AB and AB = 2MB.½ mark
2. MB² = OB² − OM² = 225 − 81 = 144, so MB = 12 cm.1 mark
3. AB = 2 × 12 = 24 cm.½ mark

Check: 9² + 12² = 81 + 144 = 225 = 15² ✓.

Answer to write in the exam

Common mistakes that cost marks

• Stopping at 12 cm (half the chord).
• Writing 15 − 9 = 6 and doubling to 12 cm: lengths cannot be subtracted like that; use squares.
• Squaring wrongly: 15² = 225, 9² = 81.

How this can come in the exam

Try one yourself

A chord is 21 cm from the centre of a circle of radius 35 cm. Find its length.

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