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If in Delta ABC, (a -b) (s-c) = (b -c) (...

If in `Delta ABC, (a -b) (s-c) = (b -c) (s-a)`, prove that `r_(1), r_(2), r_(3)` are in A.P.

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Given, `(a-b) (s-c) = (b-c) (s-a)`
`:. (a -b)/(s-a) = (b-c)/(s-c)`
`rArr ((s-b)-(s-a))/((s-a)(s-b)) = ((s-c)-(s-b))/((s-b) (s-c))`
`rArr (1)/(s -a) - (1)/(s -b) = (1)/(s-b) - (1)/(s-c)`
`rArr (Delta)/(s-a) - (Delta)/(s-b) = (Delta)/(s-b) - (Delta)/(s-c)`
`rArr r_(1) - r_(2) = r_(2) -r_(3)`
Hence, `r_(1), r_(2), r_(3)` are in A.P
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