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.

In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at points D, E and F respectively. If AB= 12 cm, BC= 8 cm and AC = 10 cm, find the lengths of AD, BE and CF.

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

The sides AB and AC are equal of an isosceles triangle ABC. D E and F are the mid-points of sides BC, CA and AB respectively. Prove that: (i) Line segment AD is perpedicular to line segment EF. (ii) Line segment AD bisects the line segment EF.

Incircle of DeltaABC touches the sides BC, AC and AB at D, E and F, respectively. Then answer the following question angleDEF is equal to

Incircle of DeltaABC touches the sides BC, AC and AB at D, E and F, respectively. Then answer the following question The length of side EF is

ABC is a triangle A line is drawn parallel to BC to meet AB and AC in D and E respectively. Prove that the median through A bisects DE.

Let s denotes the semi-perimeter of a DeltaABC in which BC=a, CA=b and AB=c. If a circle touches the sides BC, CA, AB, at D, E, F, respectively. Prove that BD=s-b.

A circle is touching the side BC of a triangle ABC at point P and touching AB and AC produced at Q and R respectively. Prove that AQ=(1)/(2)("perimeter of "triangle ABC).

Incircle of A B C touches the sides BC, CA and AB at D, E and F, respectively. Let r_1 be the radius of incircle of B D Fdot Then prove that r_1=1/2((s-b)sinB)/((1+sin(B/2)))

In figure E is a point on side CB produced of an isosceles triangle ABC with AB = AC . If A D_|_B C and E F_|_A C , prove that DeltaA B D ~DeltaE C F .