`C F` is the internal bisector of angle `C` of ` A B C` , then `C F` is equal to `(2a b)/(a+b)cosC/2` (b) `(a+b)/(2a b)cosC/2` ` (c) (b sinA)/(sin(B+C/2))` (d) none of these

In A B C with fixed length of B C , the internal bisector of angle C meets the side A Ba tD and the circumcircle at E . The maximum value of C D.D E is c^2 (b) (c^2)/2 (c) (c^2)/4 (d) none of these

The area of a parallelogram formed by the lines a x+-b x+-c=0 is (a) (c^2)/((a b)) (b) (s c^2)/((a b)) (c) (c^2)/(2a b) (d) none of these

With usual notations, in triangle A B C ,acos(B-C)+bcos(C-A)+c"cos"(A-B) is equal to(a) (a b c)/R^2 (b) (a b c)/(4R^2) (c) (4a b c)/(R^2) (d) (a b c)/(2R^2)

In triangle A B C ,a , b , c are the lengths of its sides and A , B ,C are the angles of triangle A B Cdot The correct relation is given by (a) (b-c)sin((B-C)/2)=acosA/2 (b) (b-c)cos(A/2)=as in(B-C)/2 (c) (b+c)sin((B+C)/2)=acosA/2 (d) (b-c)cos(A/2)=2asin(B+C)/2

If in the expansion of (1+x)^n ,a ,b ,c are three consecutive coefficients, then n= (a c+a b+b c)/(b^2+a c) b. (2a c+a b+b c)/(b^2-a c) c. (a b+a c)/(b^2-a c) d. none of these

In A B C , internal angle bisector of /_A meets side B C in DdotD E_|_A D meets A C in Ea n dA B in Fdot Then A E is HdotPdot of b and c A D=(2b c)/(b+c)cosA/2 E F=(4b c)/(b+c)sinA/2 (d) A E Fi si sos c e l e s

If a, b, c, d are in G.P., then (a + b + c + d)^(2) is equal to

In any triangle A B C ,sin^2A-sin^2B+sin^2C is always equal to (A) 2sinAsinBcosC (B) 2sinAcosBsinC (C) 2sinAcosBcosC (D) 2sinAsinBsinC

In triangle A B C ,/_A=30^0,H is the orthocenter and D is the midpoint of B Cdot Segment H D is produced to T such that H D=D Tdot The length A T is equal to a. 2B C b. 3B C c. 4/2B C d. none of these

In triangle A B C ,2a csin(1/2(A-B+C)) is equal to a^2+b^2-c^2 (b) c^2+a^2-b^2 (c) b^2-c^2-a^2 (d) c^2-a^2-b^2