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Manipal MET2013MathematicsProperties of Triangles

In an equilateral triangle, the in-radius, circum-radius and one of the ex-radii are in the ratio

Options

  1. A2: 3: 5
  2. B1: 2: 3
  3. C1: 3: 7
  4. D3: 7: 9

Correct answer

B. 1: 2: 3

Step-by-step solution

We have; = 3 4 a^2, s= 3 a 2 r= S = a 2 3 , R= a b c 4 = a^3 3 a^2 = a 3 and r₁= S-a = 3 / 4 a^2 a / 2 = 3 2 a Hence; r: R: r₁= a 2 3 : a 3 : 3 2 a=1: 2: 3

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