Question

If points $A, B$ and $C$ are represented by $z_1, z_2$ and $z_3$ on argand plane and all of them lie on $|z|=6$, then orthocentre of $\triangle ABC$ is given by:

• A. 0
• B. $\frac{z_1+z_2+z_3}{3}$
• C. $z_1+z_2+z_3$
• D. information is insufficient

Answer 1

Answer: (C)

$z_1+z_2+z_3

Answer 2

Given that $A$, $B$, and $C$ lie on the circle $|z|=6$, the circumcentre of $\triangle ABC$ is the origin. For any triangle with its circumcentre at the origin, the orthocentre $H$ is given by

$$H = z_1 + z_2 + z_3.$$