In a `"Delta"A B C ,` let `a ,b ,` and `c` denote the length of sides opposite to vertices A, B, and C respectively. If `b=2,c=sqrt(3)` and `/_B A C=pi/6,` then value of circumradius of triangle ABC is- `1/2` (2) 1 (3) 2 (4) `1/4`

Consider a DeltaABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C, repectively. if a=1,b=3 and C=60^(@), then sin ^(2) B is equal to

Consider a Delta ABC and let a,b, and c denote the leghts of the sides opposite to vertices A,B and C, respectively. Suppose a=2,b =3, c=4 and H be the orthocentre. Find 15(HA)^(2).

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

Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C, respectivelu. Suppose a = 6, b = 10 and the triangle is 15 sqrt3 . If angle ACB is obtus and if r denotes than radius of the incircle of the triangle, then the value of r^(2) is _____

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)

If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression (a)/(c) sin 2C + (c)/(a) sin 2A is

If circumradius of triangle is 2, then the maximum value of (abc)/(a+b+c) is

Three vertices of a triangle are A (1, 2), B (-3, 6) and C(5, 4) . If D, E and F are the mid-points of the sides opposite to the vertices A, B and C, respectively, show that the area of triangle ABC is four times the area of triangle DEF.

In a triangle ABC,a/b=2+sqrt(3) and /_C=60^(@) then angle A and B is