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The exradii r1,r2 and r3 of /\A B C are...

The exradii `r_1,r_2` and `r_3` of ` /_\A B C` are in H.P.show that its sides are in A.P .

Text Solution

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Since, `r_(1), r_(2)" and r_(3)` are exradii of `DeltaABC` are in HP.
`:." "1/r_(1),1/r_(2),1/r_(3)" are in AP"`
`rArr" "(s-a)/Delta,(s-b)/Delta,(s-c)/Delta" are in AP"`
`rArr" "s-a, s-b, s-c" are in AP".`
`rArr" -a, -b, -c are om AP".`
`rArr" a, b, c are in AP".`
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