If the angle `A ,Ba n dC` of a triangle are in an arithmetic propression and if `a , ba n dc` denote the lengths of the sides opposite to `A ,Ba n dC` respectively, then the value of the expression `a/csin2C+c/asin2A` is (a) `1/2` (b) `(sqrt(3))/2` (c) `1` (d) `sqrt(3)`

Let A B C be a triangle such that /_A C B=pi/6 and let a , b and c denote the lengths of the side opposite to A , B ,and C respectively. The value(s) of x for which a=x^2+x+1,b=x^2-1,\and\ c=2x+1 is(are) -(2+sqrt(3)) (b) 1+sqrt(3) (c) 2+sqrt(3) (d) 4sqrt(3)

Let the angles A , Ba n dC of triangle A B C be in AdotPdot and let b : c be sqrt(3):sqrt(2) . Find angle Adot

Consider a triangle A B C and let a , ba n dc denote the lengths of the sides opposite to vertices A , B ,a n dC , respectively. Suppose a=6,b=10 , and the area of triangle is 15sqrt(3)dot If /_A C B is obtuse and if r denotes the radius of the incircle of the triangle, then the value of r^2 is

In triangle A B C ,/_A=60^0,/_B=40^0,a n d/_C=80^0dot If P is the center of the circumcircle of triangle A B C with radius unity, then the radius of the circumcircle of triangle B P C is (a) 1 (b) sqrt(3) (c) 2 (d) sqrt(3) 2

Vertices of a variable acute angled triangle A B C lies on a fixed circle. Also, a ,b ,ca n dA ,B ,C are lengths of sides and angles of triangle A B C , respectively. If x_1, x_2a n dx_3 are distances of orthocenter from A ,Ba n dC , respectively, then the maximum value of ((dx_1)/(d a)+(dx_2)/(d b)+(dx_3)/(d c))+11 is a. -sqrt(3) b. 11-3sqrt(3) c. 11+6sqrt(3) d. 3sqrt(3)

A variable plane passes through a fixed point (a,b,c) and meets the axes at A ,B ,a n dCdot The locus of the point commom to the planes through A ,Ba n dC parallel to the coordinate planes is

If A ,Ba n dC are the vetices of a triangle A B C , then prove sine rule a/(sinA)=b/(sinB)=c/(sinC)dot

If the sides of a right-angled triangle are in A.P., then the sines of the acute angles are 3/5,4/5 b. 1/(sqrt(3)),sqrt(2/3) c. 1/2,(sqrt(3))/2 d. none of these

In A B C , right-angled at C , if tanA=sqrt((sqrt5-1)/2) , show that the sides a , ba n dc are in G.P.

In a triangle A B C , the bisectors of angles Ba n dC lies along the lines x=y a n d y=0. If A is (1,2) , then the equation of line B C is