In the given figure, x is (a) `(ab)/(a+b) (b) (ac)/(b+c) (c) (bc)/(b+c) (d) (ac)/(a+c)`

In DeltaABC , if (sin A)/(c sin B) + (sin B)/(c) + (sin C)/(b) = (c)/(ab) + (b)/(ac) + (a)/(bc) , then the value of angle A is

In a triangle ABC, 2B= A + C and b^(2) = ac , then (a(a+b+c))/(3bc) is

In Figure, it is given that A B=C D\ a n d\ A D=B C. Prove that A D C\ ~= C B A .

if a : b = c : d prove that : (a^(2) + ac + c^(2)) : (a^(2) - ac + c^(2)) = (b^(2) + bd + d^(2)) : (b^(2) - bd + d^(2))

If a, b, c are non zero complex numbers satisfying a^(2) + b^(2) + c^(2) = 0 and |(b^(2) + c^(2),ab,ac),(ab,c^(2) + a^(2),bc),(ac,bc,a^(2) + b^(2))| = k a^(2) b^(2) c^(2) , then k is equal to

If distinct and positive quantities a ,b ,c are in H.P. then (a) b/c= (a-b)/(b-c) (b) b^2>ac (c) b^2< ac (d) a/c=(a-b)/(b-c)

Suppose A, B, C are defined as A = a^(2)b + ab^(2) - a^(2)c - ac^(2), B = b^(2)c + bc^(2) - a^(2)b - ab^(2) , and C = a^(2)c + ac^(2) - b^(2)c - bc^(2) , where a gt b gt c gt 0 and the equation Ax^(2) + Bx + C = 0 has equal roots, then a, b, c are in

In a /_\ A B C , A D is the bisector of /_A , meeting side B C at D . (i) If AB=10 cm , AC=14 cm and BC=6cm , find B D and D C (ii) If A C=4. 2 c m , D C=6c m and B C=10 c m , find A B . (iii) If A B=5. 6 c m , A C=6c m and D C=3c m , find B C .

In figure D is a point on side BC of a DeltaA B C such that (B D)/(C D)=(A B)/(A C) . Prove that AD is the bisector of /_B A C .

If the four consecutive coefficients in any binomial expansion be a, b, c, d, then prove that (i) (a+b)/a , (b+c)/b , (c+d)/c are in H.P. (ii) (bc + ad) (b-c) = 2(ac^2 - b^2d)