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BITSAT2011MathematicsProperties of TrianglesActual

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

Options

  1. A(2: 3: 5 )
  2. B(1: 2: 3 )
  3. C(3: 7: 9 )
  4. D(3: 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 = abc 4 = a ^3 3 a ^2 = a 3 ) and (r₁= s-a = 3 / 4 a^2 a / 2 = 3 2 a ) Hence, ( r : R : r ₁= a 2 3 : a 3 : 3 2 a =1: 2: 3 )

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