Question

Locus of the centres of the circles passing through two fixed points A and B is ______.

Options

• a line parallel to line segment AB.

• the bisector of line segment AB.

• perpendicular to line segment AB.

• perpendicular bisector of line segment AB.

Answer 1

Locus of the centres of the circles passing through two fixed points A and B is perpendicular bisector of line segment AB. 

Explanation:

Let O and O' be the center of the circles, passing through points AB.

Steps of construction:

1. Join AB.
2. Draw a perpendicular from O to AB and O' to AB.

We know that,

Perpendicular from center to chord bisects it.

Since, both perpendiculars bisects AB.

∴ OO' is a straight line perpendicular to AB and bisecting it.