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AP EAMCET20227 Jul 2022Morning ShiftMathematicsProperties of TrianglesActual

In a A B C, a: b: c=4: 5: 6 . The ratio of radius of the circumcircle to that of the incircle is

Options

  1. A7: 16
  2. B17: 16
  3. C16: 17
  4. D16: 7

Correct answer

D. 16: 7

Step-by-step solution

Given, a 4 = b 5 = c 6 =k (say) a=4 k, b=5 k, c=6 ks= a+b+c 2 = 15 k 2 = s(s-a)(s-b)(s-c) = 15 k 2 7 k 2 5 k 2 3 k 2 = 15 7 k^2 4 Now, r= s = 15 7 k^2 / 4 15 k / 2 = 7 k 2 and R= a b c 4 = 8 7 k R r = 8 k 7 7 k 2 = 16 7

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