Let `A ,B ,C ,D` be four concyclic points in order in which `A D : A B=C D : C Bdot` If `A ,B ,C` are repreented by complex numbers `a ,b ,c` representively, find the complex number associated with point `Ddot`

Set A={a,b,c,d} then the number of defined relation in A is

a ,b ,c are three complex numbers on the unit circle |z|=1, such that a b c=a+b+c dot Then find the value of |a b+b c+c a|dot

If a,b,c,d are distinct positive numbers in AP, then

A , B , C , D are any four points, prove that vec A Bdot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=4(Area \ of triangle ABC).

In triangle A B C ,D is on A C such that A D=B C' and BD=D C ,/_D B C=2x ,a n d/_B A D=3x , all angles are in degrees, then find the value of x

If |z|=1, then the point representing the complex number -1+3z will lie on a. a circle b. a parabola c. a straight line d. a hyperbola

Let a ,b and c be real numbers such that a+2b+c=4 . Find the maximum value of (a b+b c+c a)dot

If vec a , vec b , vec c , vec d are the position vector of point A , B , C and D , respectively referred to the same origin O such that no three of these point are collinear and vec a + vec c = vec b + vec d , than prove that quadrilateral A B C D is a parallelogram.

Find distace between the points (a+b,c-d) and (a-b,c+d).

If a,b,c,d are odd natural numbers such that a+b+c+d=20 then the number of values of ordered quadruplet (a,b,c,d) is