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In a triangle ABC if a: b: c= 4:5:6 then...

In a triangle ABC if a: b: c= 4:5:6 then ratio between its circumradius and inredius is

A

`16/7`

B

`16/9`

C

`7/16`

D

`11/7`

Text Solution

Verified by Experts

`R/r=(abc)/(4Delta)//Delta/s=((abc)s)/(4Delta^2 )rArrR/r=(abc)/(4(s-a)(s-b)(s-c)).....(i)`
`therefore a:b:c=4 : 5:6 rArr a/4=b/5=c/6=k`(say)
`rArr a=4k,b=5k , c=6k `
`therefore s=(a+b+c)/(2)=(15k)/(2),s-a=(7k)/(2).s-b=(5k)/(2), s-c =(3k)/(2)`
using (i) these values `R/r=((4k)(5k)(6k))/(4((7k)/2)((5k)/(2))((3k)/2))=16/7`
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