Basic properties of circles・Form 4 maths

Chord problems

A standard method from Basic properties of circles: the steps and worked examples.

Steps

Draw the perpendicular from O to the chord. It bisects the chord, and gives a right-angled triangle for Pythagoras: r² = d² + (half-chord)².

Worked examples

Example 1: A circle has radius 10 cm. Chord AB = 16 cm. Find the distance from the centre O to AB.

Let M be the foot of the perpendicular from O to AB.
AM = 16 ÷ 2 = 8 cm           (line from centre ⊥ chord bisects chord)
OM = √(10² − 8²) = 6 cm      (Pythagoras' theorem)

For the whole topic, read Basic properties of circles: key points, common mistakes and how the DSE tests it.

Steps

Worked examples

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