Question

- Let 's' denotes the semi-perimeter of a ABC in which BC = a, CA = b, AB = c. If a circle
touches the sides BC, CA, AB at D, E, F respectively, prove that BD = S-b.​

Answer 1

Answer:

R.E.F image

Let BD = X as shown in the figure.

BD = BF = X (Tangents drawn from the same point B to the in circle)

Similarly, CD = CE = z and AF = AE = Y

Perimeter of the triangle is 2(x+y+z) = 2s

⇒x+y+z=s

⇒x=s−(y+z)

⇒x=s−AC

⇒x=s−b