Let s denote the semi-perimeter of `DeltaABC` where `BC=a, CA=b`, and `AB=c`. If a circle touches the sides BC, CA, and AB at D, E, and F respectively, prove that `BD= s-b`.

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 .

In the given figure, a circle is inscribed in a DeltaABC such that it touches the sides AB, BC, and CA at points D, E, and F respectively. If the lengths of the sides AB, BC, and CA are 12 cm, 8 cm, and 10 cm respectively, find the lengths of AD, BE, and CF.

If the veactors veca, vecb and vecc form the sides BC,CA and AB respectively of triangle ABC, then :

If D, E and F be the middle points of the sides BC,CA and AB of the DeltaABC , then AD+BE+CF is

In a Δ ABC, D,E,F are respectively, the mid- points of BC,CA, and AB. If the lengths of side AB, BC and CA are 7 cm, 8 cm, 9 cm, respectively, find the perimeter of Δ DEF.

In Fig , ABC and AMP are two right triangles, right angled at B and M respectively. Prove that : (CA)/(PA)=(BC)/(MP)

In DeltaABC and DeltaDEF , AB= DE, AB abs DE, BC= EF and BC abs EF . Vertices A, B and C are joined to vertices D, E and F respectively. Show that AC= DF

ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram.

If D , E and F are the mid-points of the sides BC , CA and AB respectively of the DeltaABC and O be any point, then prove that OA+OB+OC=OD+OE+OF

In DeltaABC and DeltaDEF , AB= DE, AB abs DE, BC= EF and BC abs EF . Vertices A, B and C are joined to vertices D, E and F respectively. Show that DeltaABC~=DeltaDEF .