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

Question:

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.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

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

See More Books

Question Posted: Aug 10, 2023 04:25 AM

See More Questions

The diagram shows a sector OAB of a circle with centre O and radius r. Angle AOB is radians. The point C on OA is such that BC is perpendicular to OA. The point D is on BC and the circular arc AD...
The diagram shows a sector OAB of a circle with centre O and radius r cm. The angle AOB is radians and the perimeter of the sector is 30 cm. a) Show that = 30/r 2. b) Find the area of the sector...
The diagram shows a sector OAB of a circle, centre O and radius r cm. The length of the arc AB is p cm and AOB is radians. a. Find in terms of p and r. b. Deduce that the area of the sector is 1/2...
Serra do Mar Corporation manufactures and distributes leisure clothing. Selected transactions completed by Serra do Mar during the current fiscal year are as follows: Jan. 8 Split the common stock 3...
As of June 30, 2012 (the computation date for the 2013 tax rate), Amanda Company had a negative balance of $1,015 in its unemployment reserve account in State A. The company's average payroll over...
Decide whether something is wrong with each of the graphs shown in Problems 13-17. Explain your reasoning. Consider the graph shown in Figure 14.19. Clearly, Anacin is better. ANACIN BUFFERED ASPIRIN...
Rent is apportioned based on the floor area.
Duval Manufacturing recently reported the following information: Net income $600,000 ROA 8% Interest expense $225,000 Duvals tax rate is 35%. What is its basic earning power (BEP)?
If I try to increase the market share of the companys products, I am doing the best interest of my companys shareholders says Sarah, a fresh graduate who recently joined the finance team of a public...
Of the following, what would be considered a best practice when performing risk assessments? A. Starting with clear goals and a defined scope B. Enlisting support of senior management C. Repeating...
An IT security team leader is working on a qualitative risk assessment for her company. She is thinking about the final report. What should the IT security team leader consider when providing the...
What has been the major problem in determining grazing capacity on rangelands? a. Lack of good information on how much livestock eat b. Lack of knowledge on how much use range plants can withstand c....
# III: Worksheet 3 1. A 20 kg mass is allowed to accelerate down a frictionless 15 ramp. 20 kg 15 a. Draw a force diagram for the block. b. Determine the value of the x-component of the force of...
3.Baker Corporation has provided the following production and average cost data for two levels of monthly production volume. The company produces a single product Production Volume: 1,000 units:...
Suppose that you own the only company in the market to produce a certain product, and therefore you can determine the market price P dollars for each unit. Due to government regulations, the price of...
describes how the blast pressure front can bounce off solid, immovable obstacles and be redirected in another direction in a linear angle to the angle of the obstacle hat was struck
As the accounting clerk, you are tasked by the CFO to determine the cost of goods sold of Del Mundo Company for the year ended December 31, 2020. During Operating cost data annd inventory account...
Watch Corporation has U.S. source income for the current year of $2 million, foreign source income from Country X of $3 million, and foreign source income from Country Y of $1 million, for total...
Whats the difference between an ordinary annuity and an annuity due? What type of annuity is shown below? How would you change the time line to show the other type of annuity?
Suppose we know penicillin G at a daily dose of 4.8 megaunits has a 10% failure rate. What can be said in comparing the two drugs? Sexually Transmitted Disease Suppose a clinical trial is conducted...
Find a 95% CI for the population mean concentration? Pharmacology Suppose we want to estimate the concentration (g/mL) of a specific dose of ampicillin in the urine after various periods of time. We...
Find a 99% CI for the population variance of the concentrations? Pharmacology Suppose we want to estimate the concentration (g/mL) of a specific dose of ampicillin in the urine after various periods...
Comfort Golf Products is considering whether to upgrade its equipment Managers are considering two options. Equipment manufactured by Stenback Inc. costs $1,000,000 and will last five years and have...
Weaver Corporation had the following stock issued and outstanding at January 1, Year 1: 71,000 shares of $10 par common stock. 8,500 shares of $60 par, 6 percent, noncumulative preferred stock. On...
Read the following case and then answer questions On 1 January 2016 a company purchased a machine at a cost of $3,000. Its useful life is estimated to be 10 years and then it has a residual value of...

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

Students also viewed these Mathematics questions