Question

A and B are two fixed points. What will be the locus of the point P such that $\angle APB={90}^{\circ }$

• A. The locus of point P is the perpendicular bisector of line joining AB.
• B. The locus of point P is the circumference of a circle with AB as the diameter.
• C. The locus of point P is the circumference of a semi-circle with AB as the diameter.
• D. The locus of P is any circle passing through the points A and B.

Answer 1

The correct option is B

The locus of point P is the circumference of a circle with AB as the diameter.

Join AB and draw a circle with AB as diameter. The locus of point P is the circumference of this circle, since the angle in a semi circle is ${90}^{\circ }$.
Therefore, whatever be the position of point P, the measure of $\angle APB$ will always be ${90}^{\circ }$.