Question

if 's' denotes the semi-perimeter of the triangle ABC in which BC='a' , AC='b' and AB='c' . if a circle touches the sides BC, CA and AB at the points D, E, F respectively. Prove that 'BD=s-b'

Answer 1

BF=BD
AF=AE
ADD THEM
c=BD+AE(1)

AE=AF
EC=DC
ADD THEM
b=AF+DC(2)
(1)-(2)
we get
c-b=BD-DC (AE=AF)
=BD-(BC-BD)
c-b=2BD-BC
c-b+a=2BD (a=BC)
BD=a-b+c/2


ALSO s-b=same
H.P