The incircle of an isoceles triangle ABC, with AB=AC, touches the sides AB,BC and CA at D,E and F respecrively. Prove that E bisects BC.

The incircle of an isosceles triangle ABC , with AB=AC , touches the sides AB , BC , CA at D,E and F respectively. Prove that E bisects BC .

The incircle of an isosceles triangle ABC, in which AB = AC, touches the sides BC, CA and AB at D, E and F respectively . Prove that BD = DC.

The incircle of an isosceles triangle ABC in which AB=AC , touches the sides BC, CA, and AB at D, E, and F respectively. Prove that BD=DC .

The incircle of a triangle ABC touches the sides AB, BC and CA at the points F, D and E resepectively. Prove that AF + BD + CE + DC + EA = 1/2 (Perimeter of triangle ABC)

Let the incircle of a Delta ABC touches sides BC, CA and AB at D,E and F, respectively. Let area of Delta ABC be Delta and thatof DEF be Delta' . If a, b and c are side of Detla ABC , then the value of abc(a+b+c)(Delta')/(Delta^(3)) is (a) 1 (b) 2 (c) 3 (d) 4

Let the incircle of a Delta ABC touches sides BC, CA and AB at D,E and F, respectively. Let area of Delta ABC be Delta and thatof DEF be Delta' . If a, b and c are side of Dela ABC , then the value of abc(a+b+c)(Delta')/(Delta^(3)) is

Let's denote the semi-perimeter of a triangle ABC in which BC = a, CA = 5, AB = c. If a circle touches the side BC, CA, AB at D, E, F respectively, prove that BD = S-b.

In Fig.10.19 ,the incircle of ABC touches the sides BC,CA and AB at D,E and F respectively.Show that AF+BD+CE=AE+BF+CD=(1)/(2)(Perimeter of ABC) (FIGURE)