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In triangle A B C , if cosA+cosB+cosC=7/...

In triangle `A B C ,` if `cosA+cosB+cosC=7/4, t h e n R/r` is equal to `3/4` (b) `4/3` (c) `2/3` (d) `3/2`

A

`(3)/(4)`

B

`(4)/(3)`

C

`(2)/(3)`

D

`(3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`cos A + cos B + cos C = (7)/(4)`
`rArr 1 + 4 sin.(A)/(2) sin.(B)/(2) sin.(C)/(2) = (7)/(4)`
or `4 sin.(A)/(2) sin.(B)/(2) sin.(C)/(2) = (3)/(4)`
` :' r = 4R sin(A//2) sin(B//2) sin(C//2)]`
or `(r)/(R) = (3)/(4) " or " (R)/(r) = (4)/(3)`
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