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In an equilateral triangle, the inradius...

In an equilateral triangle, the inradius, circumradius, and one of the exradii are in the ratio

A

`1:1:1`

B

`1:2:3`

C

`2:1:3`

D

`3:2:4`

Text Solution

Verified by Experts

R:r=2:1
Also
`r_(1)=r_(2)=r_(3)`
`=4RsinA/2cosB/2cosC/2=4Rxx1/2xx(sqrt3)/2xx(sqrt3)/2=3/2R`
`thereforeR:r:r_(1)=R:R/2:(3R)/2=2:1:3`
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