InterviewSolution
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InterviewSolution
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In triangle ABC, if `r_(1)+r_(2)=3R` and `r_(2)+r_(3)=2R`, thenA. `angle A =90^(@)`B. `angle B=45^(@)`C. `angle C=60^(@)`D. triangle ABC is right angled isosceles |
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Answer» Correct Answer - 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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