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

In Triangle A B C with fixed length of B C , the internal bisector of angle C meets the side A B a 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

In a triangle A B C , right angled at C ,t a n A+t a n B is equal to a. a+b b. (c^2)/(a b) c. (a^2)/(b c) d. (b^2)/(a c)

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

In a triangle A B C ,(r_1+r_2)/(1+cosC) is equal to (2a b)/(c"Delta") (b) ((a+b))/(c"Delta") (a b c)/(2"Delta") (d) (a b c)/("Delta"^2)

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)

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

If f,g,h are the internal bisectors of a /_\ ABC then 1/f cos (A/2)+ 1/g cos (B/2) +1/h cos (C/2)= (A) 1/a+1/b-1/c (B) 1/a-1/b+1/c (C) 1/a+1/b+1/c (D) none of these

In a A B C ,\ A D is the bisector of the angle A meeting B C at Ddot If I is the incentre of the triangle, then A I\ : D I is equal to - (s in B+s in C):\ s in A (b) (cos B+cos C): cos A cos((B-C)/2):cos((B+C)/2) (d) sin((B-C)/2):sin((B+C)/2)

If a ,b ,and c are in A.P., then a^3+c^3-8b^3 is equal to (a). 2a b c (b). 6a b c (c). 4a b c (d). none of these

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)=asin((B-C)/2) (c) (b+c)sin((B+C)/2)=acosA/2 (d) (b-c)cos(A/2)=2asin(B+C)/2