The distance of a chord of length 16 cm from the centre of a circle is 6 cm. Find the radius of the circle.

Step-by-step solution

Idea: The radius is the hypotenuse of the right triangle formed with the distance and half the chord.

1. OM ⟂ AB, so M is the midpoint: MB = 16 ÷ 2 = 8 cm.½ mark
2. In right ΔOMB: OB² = OM² + MB² = 36 + 64 = 100.1 mark
3. Radius OB = 10 cm.½ mark

Check: Chord = 2√(10² − 6²) = 2 × 8 = 16 cm ✓.

Answer to write in the exam

Common mistakes that cost marks

• Using 16 instead of 8: √(16² + 6²) ≈ 17.1 cm is wrong.
• Subtracting: here the radius is the hypotenuse, so the squares are added.
• Giving the diameter (20 cm) when the radius is asked.

How this can come in the exam

Try one yourself

A chord of length 96 cm is 14 cm from the centre of a circle. Find the radius.

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