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An equilateral triangle has a circle ins...

An equilateral triangle has a circle inscribed in it and is circumscribed by a circle. There is another equilateral triangle inscribed in the inner circle.Find the ratio of the areas of the outer circle and the inner equilateral triangle.

A

`(16pi)/(3sqrt(3))`

B

`(8pi)/(2sqrt(3))`

C

`(24pi)/(3sqrt(3))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
(i) Circum radius `=(a)/(sqrt(3))" and inradius " =(a)/(2sqrt(3))`.
where a is the side of the outer equilateral triangle.
(ii) For an equilateral triangle of side a, if an in-circle and circum circle are drawn whose radii are r and R then `r=(a)/(2sqrt(3)) and R=(a)/(sqrt(3)).`
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