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In any triangle ABC, find the least valu...

In any triangle ABC, find the least value of `(r_(1) + r_(2) + r_(3))/(r)`

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Verified by Experts

The correct Answer is:
9
We have already proved that `(1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3)) = (1)/(r)`
Now using A.M. `ge` H.M. we get
`(r_(1) + r_(2) + r_(3))/(3) ge (3)/((1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3))) = 3r`
`rArr (r_(1) + r_(2) + r_(3))/(r) ge 9`
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