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KVPY2014MathematicsProperties of Triangles

The angle bisectors B D and C E of a triangle A B C are divided by the incentre l in the rators 3: 2 and 2: 1 respectively. Then the ratio in which I divides the angle bisector through A is.

Options

  1. A3: 1
  2. B11: 4
  3. C6: 5
  4. D7: 4

Correct answer

B. 11: 4

Step-by-step solution

A l I F = b+c a ...... (1) B l I D = a+c b = 3 2 ...... (2) array l C l I E = a+c c = 2 1 a+b=2 c ...... (3) (2) 2 a+2 c=3 b using (2) 2 a+a+b=3 b using (3) 3 a=2 b b= 3 2 a ...... (4) array Now again (3) 2 c=a+b array l =a+ 3 2 a c+ 5 4 a array Hence A l I F = b+c a = 1 2 a+ 5 4 a a = 11 4

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