Question

Let $A$ and $B$ be two points on the edge of a semi-circle. What is the locus of the point $P$ drawn on the circle such that angle $APB={90}^{\circ }$?

• A. The line $AB$ itself
• B. The point $P$ itself
• C. The circumference of the circle with $AB$ as diameter
• D. The line perpendicular to $AB$ and bisecting $AB$

Answer 1

The correct option is C The circumference of the circle with $AB$ as diameter

Recall theorem of Thales:
i.e angles in a semicircle is a right angle.
Locus of $P$ is a circle with $AB$ as diameter.