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1. If in a triangle ABC the exradii r 1 , r 2 , r 3 , are such that r 1 = 2 r 2 = 3r 3 then a;b;c is

1. If in a triangle ABC the exradii r1, r2, r3, are such that r1 = 2r2 = 3r3  then a;b;c is 

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear

we know

    r1 = Δ /(s-a)

    r2   = Δ /(s-b)

    r3    =Δ/(s-c)

so     r1 = 2r2 = 3r3

      Δ /(s-a) =2Δ /(s-b) =3Δ /(s-c)

 

     s-b =2s-2a                and     s-c = 3s-3a

     3b +c -4a=0                and  2a -b-2c=0

solve  a/5 = b/6 =c/2

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Badiuddin

 

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