The angle biosectors BD and CE of a triangle ABC are divied by the incentre 1 in the rartios 3 : 2 and 2 : 1 respecticely. Then the ratio in which I divides the bisector through A is-

Options

A. `3 : 1`
B. `11 : 4`
C. `6 : 5`
D. `7 : 4`

Answer

B

Explanation

I divides AF
b + c : a
I divides BD
c + a : b
I divides CE in
a + b : c
`(c+a)/b=3/2, (a+b)/c=2/1`
`{:(,2c+2a=3b,"",rArra+b+=2c),(,rArra+b+2a=3b," ",a+(3a)/2=2c),(,rArr3a=2b," ",5/2a=2c),(,rArrb=(3a)/2," ",c=5/4a):}`
`"Now "(b+c)/a=((3a)/2+(5a)/4)/a=(6+5)/4=11/4`