Area enclosed by tangents and major arc

C

Colin67

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Jan 29, 2020
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Hi All

I would be grateful for help with this question:

A chord AB of a circle of radius 5a is of length 3a. The tangents to the circle at A and B meet at T. Find the area enclosed by TA, TB and the major arc AB.

Taking centre of circle as O. I have tried working out angle AOT, I get 16.69 degrees. From this I work out length AT, I get 1.499a. I then worked out are of triangle OAT as 3.74, doubled it to get area of OATB.

I then worked out area of major sector(angle was 360-33.38 degrees), as 71.25a^2.

In the end the answer I get is 78.75a^2.

I am unsure if my method is correct, the answer in the book is given as 78.79a^2.

I would appreciate advice on the correct method to answer this question.

Thanks
 
Hello, and welcome to Free Math Help!

Could you post a picture of the diagram given? It would help very much. :)
 
I haven't looked at the problem in detail yet, but could your answer be slightly off due to calculator rounding?
 
Last edited:
Dear Firemath

It's possible, but I'm not 100% sure of the method I used either.
 
Ok. No worries. :)

I would suggest looking at what you know, such as equal areas and lengths. Then work an alternative method.
 
I get a different angle at the first step. Please show details of what you did. In particular, did you use sine or tangent?
 
Colin67 said:
seen an error, angle aot is 17.45, using sine
Click to expand...
No, it's 17.4576... . If you choose to use a rounded value, be sure to round correctly. But you really should not use a rounded value in your work at all.
 
Thank you all for help, with all the corrections I have solved the problem.

Many thanks again
 
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