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AP EAMCET202125 Aug 2021Evening ShiftMathematicsProperties of TrianglesActual

In A B C , if a: b: c=4: 5: 6 , then the ratio between the circumradius and the inradius is

Options

  1. A16 7
  2. B16 9
  3. C7 16
  4. D11 7

Correct answer

A. 16 7

Step-by-step solution

Given a: b: c=4: 5: 6 To find R : r Where, R is circumradius and r is inradius. Let a + 4k, b = 5k and c = 6k aligned & s= a+b+c 2 = 15 k 2 & s-a= 15 k 2 -4 k= 7 k 2 , s-b= 5 k 2 and s-c= 3 k 2 & = s(s-a)(s-b)(s-c) = 15 k 2 7 k 2 5 k 2 3 k 2 & = 15 7 4 k^2 & R= a b c 4 = 4 k 5 k 6 k 4 15 7 4 k^2 = 8 7 k & r= s = 15 7 15 2 k k^2 = 7 2 k & R: r= 8 7 k: 7 2 k=16: 7 aligned

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