In any triangle `A B C ,(a^2+b^2+c^2)/(R^2)` has the maximum value of 3 (b) 6 (c) 9 (d) none of these

Explanation

`(a^2+b^2+c^2)/R^2=((2RsinA)^2+(2RsinB)^2+(2Rsinc)^2)/R^2`

`4(sin^2A+sin^2B+sin^2C)`

`4*2(1+cosAcosBcosC)`

`8(1+cosAcosBcosC)`

`8(1+1/8)`

`8(9/8)`

`9`

Option C is correct.