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A circle of area 20 sq. units is centere...

A circle of area 20 sq. units is centered at the point O. Suppose `DeltaABC` is inscribed in that circle and has area 8 sq. units. The central angles `alpha, beta` and `gamma` are as shown in the figure. The value of `(sin alpha+sin beta+sin gamma)` is equal to

A

`(4pi)/(5)`

B

`(3pi)/(4)`

C

`(2pi)/(5)`

D

`(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `pi R^(2)=20` (Given)
Now, `(1)/(2)R^(2)(sin alpha + sin beta + sin gamma) = 8` (Given)

`therefore sin alpha + sin beta + sin gamma = (16)/(R^(2))=((16)pi)/(20)=(4pi)/(5)`
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