IF the vertices of a triange ABC are respresented by `z_1,z_2 and z_3` respectively, show that its circumcentre is `(z_1sin2A+z_2sin2B+z_3sin2C)/(sin2A+sin2B+sin2C)`

Let z_(1),z_(2) and z_(3) represent the vertices A,B, and C of the triangle ABC , respectively,in the Argand plane,such that |z_(1)|=|z_(2)|=|z_(3)|=5. Prove that z_(1)sin2A+z_(2)sin2B+z_(3)sin2C=0

Let z_1, z_2a n dz_3 represent the vertices A ,B ,a n dC of the triangle A B C , respectively, in the Argand plane, such that |z_1|=|z_2|=|z_3|=5. Prove that z_1sin2A+z_2sin2B+z_3sin2C=0.

Let z_1, z_2a n dz_3 represent the vertices A ,B ,a n dC of the triangle A B C , respectively, in the Argand plane, such that |z_1|=|z_2|=|z_3|=5. Prove that z_1sin2A+z_2sin2B+z_3sin2C=0.

Let z_1, z_2a n dz_3 represent the vertices A ,B ,a n dC of the triangle A B C , respectively, in the Argand plane, such that |z_1|=|z_2|=|z_3|=5. Prove that z_1sin2A+z_2sin2B+z_3sin2C=0.

If z_(1) , z_(2) and z_(3) are the vertices of DeltaABC , which is not right angled triangle taken in anti-clock wise direction and z_(0) is the circumcentre, then ((z_(0)-z_(1))/(z_(0)-z_(2)))(sin2A)/(sin2B)+((z_(0)-z_(3))/(z_(0)-z_(2)))(sin2C)/(sin2B) is equal to

If z_(1) , z_(2) and z_(3) are the vertices of DeltaABC , which is not right angled triangle taken in anti-clock wise direction and z_(0) is the circumcentre, then ((z_(0)-z_(1))/(z_(0)-z_(2)))(sin2A)/(sin2B)+((z_(0)-z_(3))/(z_(0)-z_(2)))(sin2C)/(sin2B) is equal to

If z_(1) , z_(2) and z_(3) are the vertices of DeltaABC , which is not right angled triangle taken in anti-clock wise direction and z_(0) is the circumcentre, then ((z_(0)-z_(1))/(z_(0)-z_(2)))(sin2A)/(sin2B)+((z_(0)-z_(3))/(z_(0)-z_(2)))(sin2C)/(sin2B) is equal to

Show that sin (x-y) + sin (y-z) + sin (z-x) + 4sin((x-y)/(2)) sin( (y-z)/(2)) sin((z-x)/(2)) =0

Show that sin (x-y) + sin (y-z) + sin (z-x) + 4sin((x-y)/(2)) sin( (y-z)/(2)) sin((z-x)/(2)) =0