The distance between the orthocentre and circumcentre of the triangle with vertices `(1,2),\ (2,1)\ a n d\ ((3+sqrt(3))/2,(3+sqrt(3))/2)` is
a. 0 b. `sqrt(2)` c. `3+sqrt(3)` d. none of these

The incentre of a triangle with vertices (7, 1),(-1, 5) and (3+2sqrt(3),3+4sqrt(3)) is

(sqrt(-2))(sqrt(-3)) is equal to A. sqrt(6) B. -sqrt(6) C. isqrt(6) D. none of these

The orthocentre of triangle with vertices (2,(sqrt3-1)/2) , (1/2,-1/2) , (2,,-1/2)

The orthocentre of triangle with vertices (2,(sqrt3-1)/2) , (1/2,-1/2) , (2,,-1/2)

The incenter of the triangle with vertices (1,sqrt(3)),(0,0), and (2,0) is (a) (1,(sqrt(3))/2) (b) (2/3,1/(sqrt(3))) (c) (2/3,(sqrt(3))/2) (d) (1,1/(sqrt(3)))

The value of |-1 2 1 3+2sqrt(2) 2+2sqrt(2) 1 3-2sqrt(2) 2-2sqrt(2) 1| is equal to a. zero b. -16sqrt(2) c. -8sqrt(2) d. none of these

The perimeter of the triangle formed by the points (0,\ 0),\ (1,\ 0) and (0,\ 1) is 1+-sqrt(2) (b) sqrt(2)+1 (c) 3 (d) 2+sqrt(2)

Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(3)-i)/2 d. (-sqrt(3)+i)/2

The value of ("lim")_(xvec2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (d) none of these

If in a "Delta"A B C ,\ A=(0,0),\ B=(3,3sqrt(3)), C-=(-3sqrt(3),3) then the vector of magnitude 2sqrt(2) units directed along A O ,\ w h e r e\ O is the circumcentre of A B C is a. (1-sqrt(3)) hat i+(1+sqrt(3)) hat j b. (1+sqrt(3)) hat i+(1-sqrt(3)) hat j c. (1+sqrt(3)) hat i+(sqrt(3)-1) hat j d. none of these