Question

Assertion :Let ABC be a triangle inscribed in a circle $|z|=n$. Let the line drawn $\perp$ to BC through the point A meets the circle at D. Let E be the image of D in the line BC. If the complex numbers $z_1,z_2,z_3$ represent the points A, B, C respectively, then the complex number represented by E is $z_1+z_2+z_3$. Reason: The image of D in the line BC is the orthocenter of the triangle ABC.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A).
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A) is true (R) is false.
• D. (A) is false (R) is true.

Answer 1

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A).

For triangle ABC, the circumcentre is 0 & centroid is $\frac{z_1+z_2+z_3}{3}$
$\therefore$ Orthocentre is $z_1+z_2+z_3$, since the distance of orthocenter from circumcenter is thrice that of centroid from the circumcenter.
Hence option A is correct.