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
- A3: 1
- B11: 4
- C6: 5
- 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