Consider `/_\ ABC` Let I be the incentre and a,b c be the sides of the triangle opposite to the angle A,B,C respectively. Let O be any point in the plane of `/_\ ABC` within the triangle . AO ,BO ,CO meet the sides BC, CA and AB in D, E and F respectively then `(OD)/(AD) +(OE)/(BE)+ (OF)/(CF) =`

Consider /_\ABC . Let I bet he incentre and a,b,c be the sides of the triangle opposite to angles A,B,C respectively. Let O be any point in the plane of /_\ABC within the triangle. AO,BO and CO meet the sides BC, CA and AB in D,E and F respectively. If 3vec(BD)=2vec(DC) and 4vec(CE)=vec(EA) then the ratio in which divides vec(AB) is (A) 3:4 (B) 3:2 (C) 4:1 (D) 6:1

Consider /_\ABC . Let I bet he incentre and a,b,c be the sides of the triangle opposite to angles A,B,C respectively. Let O be any point in the plane of /_\ABC within the triangle. AO,BO and CO meet the sides BC, CA and AB in D,E and F respectively. avec(IA)=bvec(IB)+cvec(IC)= (A) -1 (B) 0 (C) 1 (D) 3

O is any point in the plane of the triangle ABC,AO,BO and CO meet the sides BC,CA nd AB in D,E,F respectively show that (OD)/(AD)+(OE)/(BE)+(OF)/(CF)=1.

let P an interioer point of a triangle A B C and A P ,B P ,C P meets the sides B C ,C A ,A B in D ,E ,F , respectively, Show that (A P)/(P D)=(A F)/(F B)+(A E)/(E C)dot

O is any point inside a triangle A B C . The bisector of /_A O B ,/_B O C and /_C O A meet the sides A B ,B C and C A in point D ,E and F respectively. Show that A D * B E * C F=D B * E C * F A

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.

Let a,b,c be the sides of a triangle ABC, a=2c,cos(A-C)+cos B=1. then the value of C is

Consider a Delta ABC and let a,b, and c denote the leghts of the sides opposite to vertices A,B and C, respectively. Suppose a=2,b =3, c=4 and H be the orthocentre. Find 15(HA)^(2).

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

D, E and F are the mid-points of the sides BC, CA and AB, respectively of an equilateral Delta ABC. Show that Delta DEF is also an equilateral triangle.