Shape and Space 6

2 marks · Normal

In a circle, the chord AB is 8 cm long and is perpendicular to the radius at its midpoint. If the radius of the circle is 5 cm, work out the perpendicular distance from the centre of the circle to the chord, giving your answer to 2 decimal places.

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3 cm (±0.05)

Common mistakes: Forgetting to halve the chord length

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Recognises a right triangle and applies Pythagoras' theorem.

A1 · 1 mark · Finds distance = 3.00 cm (accept 2.99–3.01 cm).

Worked solution

Let M be the midpoint of the chord.