Shape and Space 6
4 marks · NormalIn the diagram, O is the centre of the circle. The radius of the circle is 5 cm. AB and AC are chords of the circle and angle BAC = 32°.
Find the size of angle BOC. Give a reason for your answer.
Calculate the length of the chord BC. Give your answer to 2 decimal places.
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) 64° (Angle at centre is twice angle at the circumference) ° · must show twice the angle at circumference
(b) 8.98 cm · must show cosine rule
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · States that the angle at the centre is twice the angle at the circumference.
A1 (a) · 1 mark · Correctly calculates angle BOC as 64°.
M2 (b) · 1 mark · Attempts cosine rule to find BC using correct or ft angle. (follow-through)
A2 (b) · 1 mark · Obtains BC = 8.98 cm (2 dp). Accept values 8.97 to 8.99. (follow-through)
Worked solution
(a) Angle at centre theorem: angle at centre is twice the angle at the circumference.
(b) Use cosine rule in triangle BOC:
Correction: Cosine rule should be between B and C, with angle BAC subtended, using 5 and 5 and included angle 64°. Therefore: