In any triangle, the minimum value of `r_1r_2r_3//r^3` is equal to

Options

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

Explanation

Here, we will use the property G.M. is always greater than or equal to H.M.

`:. (r_1/r* r_2/r* r_3/r )^(1/3) ge 3/(r/r_1+ r/r_2+ r/r_3)->(1)`

Now, `r = Delta/s, r_1 = Delta/(s-a),r_2 = Delta/(s-b),r_3 = Delta/(s-c)`

`:. r/r_1 = (s-a)/s, r/r_2 = (s-b)/s,r/r_3 = (s-c)/s`

`:. r/r_1+r/r_2+r/r_3 = 1/s[s-a+s-b+s-c] = 1/s[3s-(a+b+c)]`

`= 1/s[3s-2s] = 1`

`:. r/r_1+r/r_2+r/r_3 = 1`

So, `(1)` becomes,

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