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. `5 : 2`
B. `5 : 4`
C. `5 : 3`
D. `3 : 2`

Answer

A

Explanation

Area of the triangle, `Delta k^(2) sqrt(11 xx 6 xx 3 xx 2) = 6 sqrt11 k^(2)`
So, `r = (Delta)/(s) = (6)/(sqrt11) k`
And, `R = (abc)/(4Delta) = (5 xx 8 xx 9)/(4 xx 6 xx sqrt11) k = (15)/(sqrt11) k`
`:. R : r = 5 : 2`