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In Delta ABC, if r(1) lt r(2) lt r(3), t...

In `Delta ABC`, if `r_(1) lt r_(2) lt r_(3)`, then find the order of lengths of the sides

Text Solution

Verified by Experts

The correct Answer is:
`a lt b lt c`
In `DeltaABC`, we have `r_(1) lt r_(2) lt r_(3)`. Thus,
`(1)/(r_(1)) gt (1)/(r_(2)) gt (1)/(r_(3))`
`rArr (s -a)/(Delta) gt (s-b)/(Delta) gt (s -c)/(Delta)`
`rArr s -a gt s-b gt s-c`
`rArr -a gt -b gt -c`
or `a lt b lt c`
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Knowledge Check

  • In Delta ABC , if r_(1)=r_(2)+r_(3)+r , then triangle is

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