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In a !ABC , if 2R + r = r(1) , then...

In a `!ABC` , if 2R + r =` r_(1)` , then

A

`angleA=pi//2`

B

`angleB=pi//2`

C

`angleC=pi//2`

D

none of these

Text Solution

Verified by Experts

We have,
`2R=r=r_(1)`
`rArr2R=r_(1)-r`
`rArr2R=4RsinA/2cosB/2cosC/2-4RsinA/2sinB/2sinC/2`
`rArr2R=4RsinA/2cos((B+C)/2)`
`rArr1=2sin^(2)A/2rArrsinA/2=1/(sqrt2)rArrA/2=(pi)/4rArrA=(pi)/2`
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