In `DeltaABC, R, r, r_(1), r_(2), r_(3)` denote the circumradius, inradius, the exradii opposite to the vertices A,B, C respectively. Given that `r_(1) :r_(2): r_(3) = 1: 2 : 3`
The sides of the triangle are in the ratio

Options

A. `1 : 2 : 3`
B. `3 : 5 : 7`
C. `1 : 5 : 9`
D. `5 : 8 : 9`

Answer

D

Explanation

`(Delta)/(s-a) : (Delta)/(s-b): (Delta)/(s-c) = 1: 2:3`
Let `(Delta)/((s-a)/(1)) = (Delta)/((s-b)/(2)) = (Delta)/((s-c)/(3)) = (Delta)/(6k)`
`rArr (1)/(s-a) = (1)/(6k), (1)/(s-b)= (1)/(3k), (1)/(s-c) = (1)/(2k)`
`rArr s-a = 6k, s-b = 3k, s-c = 2k`
`rArr s= 11k`
`:. a = 5k, b= 8k, c = 9k`
Hence, ratio of sides is `5: 8: 9`