Shape and Space 2
4 marks · HardThe diagram below shows a circle with centre O. The point M is the midpoint of chord AB. AB = 14 cm and OM = 6 cm.
Work out the radius of the circle.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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The radius is 10 cm. cm (±0.1)
Also accept: 10.0 cm with clear correct working; 9.97 cm if using more precise working
Common mistakes: Forgetting to halve the chord; Incorrect application of Pythagoras
Show mark scheme and worked solution
Marking points
M1 · 1 mark · States or uses the property that the perpendicular from O to AB bisects AB (AM = MB = 7 cm).
M2 · 1 mark · Applies Pythagoras’s Theorem to triangle OMA (OM² + AM² = OA²).
A1 · 1 mark · Correct substitution: 6² + 7² = OA², or equivalent.
A2 · 1 mark · Evaluates to OA = 10 cm (allow small rounding errors).
Worked solution
OM is perpendicular from the centre to the chord AB, so it bisects AB: AM = 14 ÷ 2 = 7 cm.
In right triangle OMA: OM = 6 cm, AM = 7 cm, OA = radius r.
To 2 decimal places, the radius is approximately 9.22 cm.