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In any triangle, the minimum value of r(...

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

A

1

B

9

C

27

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`((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`
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