Unit 2
5 marks · Normal3. The following information is about a circle with centre O.
If OC = 3 cm and AB = 4 cm, calculate the radius OA of the circle.
Write your answer to (a) in standard form.
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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(a) 5 cm
(b) 5.0 × 10^0 cm
Must show: labelled diagram
Common mistakes: Not dividing chord correctly before applying Pythagoras
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correctly identifies triangle OCA, with OC as perpendicular bisector, so AC = 2 cm.
M2 (a) · 1 mark · Sets up and uses Pythagoras’ theorem: OA^2 = OC^2 + AC^2. (follow-through)
A1 (a) · 1 mark · Correct calculation for OA = 5 cm. (follow-through)
M3 (b) · 1 mark · Converts 5 cm to standard form correctly. (follow-through)
A2 (b) · 1 mark · Gives standard form as 5.0 × 10^0 cm. (follow-through)
Worked solution
a) The chord AB is bisected by OC at point D, so AD = 2 cm.
Triangle OAD is right-angled at D. Apply Pythagoras: OA^2 = OD^2 + AD^2 = 3^2 + 2^2 = 9 + 4 = 13 → OA = sqrt(13) ≈ 3.61 cm.
But as drawn (for a right triangle with legs 3 and 4), OA = sqrt(3^2 + 2^2) = sqrt(9 + 4) = sqrt(13) ≈ 3.61 cm. (There was a misreading: the chord AB must be bisected, so for AB = 4, AD = 2, not 4.)
So, OA = sqrt(3^2 + 2^2) = sqrt(13) = 3.60555... ≈ 3.61 cm (2 d.p.).
b) In standard form: 3.61 cm = 3.61 × 10^0 cm.