In `ABC` with usual notations, if `r=1,r_1=7 and R=3,` the `(a) ABC` is equilateral (b) acute angled which is not equilateral (c) obtuse angled (d) right angled

Options

A. equilateral
B. acute angled which is not equilateral
C. obtuse angled
D. right angled

Answer

D

Explanation

We have `r_(1) -r 4R sin.(A)/(2) [cos.(B)/(2) cos.(C)/(2) - sin.(B)/(2) sin.(C)/(2)]`
`rArr 7 -1 = 4R sin.(A)/(2) cos ((B+C)/(2))`
`rArr 6 = 4R sin^(2).(A)/(2)`
`rArr 6 = 12 sin^(2).(A)/(2)`
`rArr sin^(2).(A)/(2) = (1)/(2)`
`rArr sin.(A)/(2) = (1)/(sqrt2)`
`rArr (A)/(2) = (pi)/(4)`
`rArr A = (pi)/(2)`