If a, b, c are sides of a triangle, then `((a+b+c)^(2))/(ab+bc+ca)` always belongs to

If a,b,c are in H.P and ab+bc+ca=15 then ca=

Let a, b, c be the sides of a triangle . No two of them are equal and λ∈R . If the roots of the equation x ^2+2(a+b+c)x+3λ(ab+bc+ca)=0 are real, then

If a,b,c are sides an acute angle triangle satisfying a^(2)+b^(2)+c^(2)=6 then (ab+bc+ca) can be equal to

If a,b,c are in A.P then a+1/(bc), b+1/(ca), c+1/(ab) are in

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

If a , b , c are all non-zero and a+b+c=0 , then (a^(2))/(bc)+(b^(2))/(ca)+(c^(2))/(ab)= ? .

If a,b,c are real numbers such that 3(a^(2)+b^(2)+c^(2)+1)=2(a+b+c+ab+bc+ca) , than a,b,c are in

The sides of triangle ABC satisfy the relations a + b - c= 2 and 2ab -c^(2) =4 , then the square of the area of triangle is ______

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) =

If a,b,c are unequal and positive then show that (bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)<1/2(a+b+c)