UPSC CDS Math Lines and Angles Questions

The angle bisector AX divide the side BC in the ratio of side AB and AC
‌

AB

AC

=‌

b

c

=‌

CX

BX

CX=‌

b⋅a

b+c

,BX=‌

c⋅a

b+c

So
‌

AB

BX

=‌

c

(‌ c⋅a b+c )

=‌

b+c

a

so we cannot define relation between AB and BX.
And
‌

BX

CX

=‌

( c⋅a b+c )

(‌ b⋅a b+c )

=‌

c

b

so we cannot define relation between BX and CX.