Question

P is a moving point and AB is a chord of a circle. If P moves, within this circle, in such a way that it is at equal distances from points A and B. The locus of P is ______.

पर्याय

• a chord perpendicular to chord AB

• a chord that bisects the chord AB

• a diameter of the circle

• the diameter of the circle which is perpendicular to chord AB

Answer 1

the diameter of the circle which is perpendicular to chord AB

Explanation:

Let O be the center of the circle and AB be the chord.

Draw XY, perpendicular bisector of AB.

We know that,

Locus of a point equidistant from two given points is the perpendicular bisector of the line joining the two points.

∴ XY is the locus of point P.

We know that,

Perpendicular to a chord passes through center of the circle.

We know that,

Chord passing through the center is the diameter.

Locus of point P is the diameter of the circle which is perpendicular to chord AB.