Given that `Delta = 6, r_(1) = 2,r_(2)= 3, r_(3) = 6`
Circumradius R is equal to a) 2.5 b)3.5 c)1.5 d)none of these

Options

A. 2.5
B. 3.5
C. 1.5
D. none of these

Answer

A

Explanation

We have,
`r_(1) = (Delta)/(s-a) = 2, r_(2) = (Delta)/(s-b) = 3, r_(3) = (Delta)/(s-c) = 6`
Given `Delta =6`,
`:. S-a = 3` ...(i)
`s-b =2` ...(ii)
`s-c =1` ...(iii)
Adding Eqs. (i) and (ii), `2s - a - b =5 " or " a + b + c -a -b = 5 or c = 5`
Adding Eqs. (i) and (iii), `2s - a- c = 4, or b = 4`
And adding Eqs. (ii) and (iii), `2s -b -c = 3 or a = 3`
Hence the sides of the `Delta` are `a =3, b = 4, c = 5`
Since the triangle is right angled, the greatest angle is `90^(@)`.
Also, the least angle is opposite to side a, which is `sin^(-1).(3)/(5)`. Therefore,
`90^(@) - "sin"^(-1)(3)/(5) = "cos"^(-1)(3)/(5)`
Also, `R = (abc)/(4Delta) = (60)/(24) = 2.5`
`r = (Delta)/(s) = (6)/(6) = 1`