In `ABC` with usual notations, if `r=1,r_1=7 and R=3,` the `ABC` is (a) 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)`