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In triangle ABC, if r(1)+r(2)=3R and r(2...

In triangle ABC, if `r_(1)+r_(2)=3R` and `r_(2)+r_(3)=2R`, then

A

`angle A =90^(@)`

B

`angle B=45^(@)`

C

`angle C=60^(@)`

D

triangle ABC is right angled isosceles

Text Solution

Verified by Experts

The correct Answer is:
A, C
`r_(1)+r_(2)=3R`
`rArr ((Delta)/(s-a))+((Delta)/(s-b))=3((abc)/(4Delta))`
`rArr(Delta^(2))/((s-a)(s-b))=(3ab)/(4)`
`rArr 4s(s-c)=3ab`
`rArr "cos"(C )/(2)=(sqrt(3))/(2)rArr angle C=60^(@)`
Also, `r_(2)+r_(3)=2R`
`rArr ((Delta)/(s-b))+((Delta)/(s-c))=2((abc)/(4Delta))`
`rArr 2s(s-a)=bc`
`rArr "cos"(A)/(2)=(1)/(sqrt(2))`
`rArr angle = 90^(@)` and `angle B = 30^(@)`
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