A,B and C are:

In Fig, if A D ,\ A E and B C are tangents to the circle at D ,\ E and F respectively. Then, (a) A D=A B+B C+C A (b) 2A D=A B+B C+C A (c) 3A D=A B+B C+C A (d) 4A D=A B+B C+C A

If a ,\ b ,\ c are real numbers such that |(b+c,c+a ,a+b),( c+a,a+b,b+c),(a+b,b+c,c+a)|=0 , then show that either a+b+c=0 or, a=b=c .

For any three vectors a,b and c prove that ["a b c"]^(2)=|(a*a,a*b,a*c),(b*a,b*b,b*c),(c*a,c*b,c*c)|

Using the factor theorem it is found that a+b , b+c and c+a are three factors of the determinant |[-2a ,a+b, a+c],[ b+a,-2b,b+c],[c+a ,c+b,-2c]| . The other factor in the value of the determinant is

If each of a, b and c is a non-zero number and (a)/(b)= (b)/(c ) , show that: (a + b+c) (a-b + c) = a^(2) + b^(2) + c^(2)

Using the factor theorem it is found that a+b , b+c and c+a are three factors of the determinant |[-2a, a+b ,a+c],[ b+a,-2b,b+c],[c+a, c+b, -2c]|dot The other factor in the value of the determinant is (a) 4 (b) 2 (c) a+b+c (d) none of these

If in a triangle A B C angle B=90^0 then tan^2(A/2) is (b-c)/a (b) (b-c)/(b+c) (c) (b+c)/(b-c) (d) (b+c)/a

If A B C\ ~= A C B , then A B C is isosceles with (a) A B=A C (b) A B=B C (c) A C=B C (d) Non e\ of\ t h e s e

If a , b ,c in Ra n da(a+b)+b(b+c)+c(c+a)=0 then a. a=b=c=0 b. a+b+c+=0 c. (a-b)^2+(b-c)^2+(c-a)^2=0 d. a^3+b^3+c^3+3a b c=0

In A B C , ray A D bisects /_A and intersects B C in D . If B C=a , A C=b and A B=c , prove that B D=(a c)/(b+c) (ii) D C = (a b)/(b+c)