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The ex-radii r1,r2,r3 or Delta ABC are ...

The ex-radii `r_1,r_2,r_3` or `Delta ABC` are in H.P. Show that its sides a,b,c are in A.P.

Text Solution

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