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In an equilateral triangle the ratio of ...

In an equilateral triangle the ratio of circum-radius and in-radius is

A

`3:1`

B

`1:1`

C

`2:sqrt3`

D

`2:1`

Text Solution

Verified by Experts

Let a be the length of each side of an equilateral triangle ABC. Then,
`R=a/(2sinA)=a/(2xx(sqrt3)/2)=a/(sqrt3)`
and, `r=(s-a)tanA/2=a/2tanpi/6=a/(2sqrt3)`
`thereforeR:r=2:1`
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