In ` A B C ,A(z_1),B(z_2),a n dC(z_3)` are inscribed in the circle `|z|=5.` If `H(z_n)` be the orthocenrter of triangle `A B C` , then find `z_ndot`

In Delta ABC,A(z_(1))B(z_(2))C(z_(3)) is inscribed in a circle |z|=5. If H(z_(H)) be the orthocentre of triangle ABC z_(H)

A(z_(1)),B(z_(2)) and C(z_(3)) are the vertices of triangle ABC inscribed in the circle |z|=2, internal angle bisector of angle A meets the circumcircle again at D(z_(4)). Point D is:

If z_(1),z_(2),z_(3) are vertices of an equilateral triangle inscribed in the circle |z|=2 and if z_(1)=1+iota sqrt(3), then

If A(z_(1)),B(z_(2)), C(z_(3)) are the vertices of an equilateral triangle ABC, then arg (2z_(1)-z_(2)-z_(3))/(z_(3)_z_(2))=

Let vertices of an acute-angled triangle are A(z_(1)),B(z_(2)), and C(z_(3))* If the origin O is he orthocentre of the triangle,then prove that z_(1)(bar(z))_(2)+(bar(z))_(1)z_(2)=z_(2)(bar(z))_(3)+(bar(z))_(2)z_(3)=z_(3)(bar(z))_(1)+(bar(z))_(3)z_(1)

A(z_a), B(z_b), C(z_c) are vertices of right angled triangle, zc being the orthocentre. A circle is described on AC as di- ameter. Find the point of intersection of the circle with hypotenuse.

Let z, and z_(1)=(a)/(1-1),z_(2)=(b)/(2+1) and z_(3)=a-ib for a,b in R. If z_(1),z_(2)=1, then the centroid of the triangle formed by the points z_(1),z_(2) and z_(3), in the argand plane is given by