In any triangle, the minimum value of `r^(3) /(r_(1) r_(2) r_(3))` is equal to

Options

A. 1
B. 1/9
C. 1/27
D. none of these

Answer

C

Explanation

`((r_(1))/(r)(r_(2))/(r)(r_(3))/(r))^(1//3) ge (3)/((r)/(r_(1)) + (r)/(r_(2)) + (r)/(3))` (using G.M. `ge` H.M.)
`ge (3)/((s-a)/(s) + (s-b)/(s) + (s-c)/(s)) ge (3s)/(s-a+s -b + s-c) ge (3s)/(s)`
`rArr (r_(1))/(r) (r_(2))/(r) (r_(3))/(r) ge 27`