In the diagram OAB is a sector of a circle, centre O and radius R cm, and

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In the diagram OAB is a sector of a circle, centre O and radius R cm, and ∠AOB = 2θ radians. A circle, centre C and radius r cm, touches the arc AB at T, and touches OA and OB at D and E respectively, as shown.

a. Write down, in terms of R and r, the length of OC.

b. Using △OCE, show that R sin θ = r (1 + sin θ).

c. Given that sin θ = 3/4 and that the perimeter of the sector OAB is 21 cm, find r, giving your answer to 3 significant figures.

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Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

ISBN: 9781292183404

1st Edition

Authors: Greg Attwood, Jack Barraclough, Ian Bettison, David Goldberg, Alistair Macpherson, Joe Petran

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Question Posted: Aug 10, 2023 04:25 AM

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In the diagram OAB is a sector of a circle, centre O and radius R cm, and

Question:

D Rcm rcm E T B

Step by Step Answer:

a To find the length of OC we can use the Pythagorean theorem in triangle ODC OC2 OD2 DC2 Since OD R ...View the full answer

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

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