Question

The locus of the centres of the circles passing through two fixed points $A$ and $B$ is

• A. the circle whose diameter is $AB$
• B. the circle with a diameter perpendicular to $AB$
• C. the perpendicular bisector of the line $AB$
• D. none of the above

Answer 1

Answer: (C)

the perpendicular bisector of the line $AB$

Let O be the centre of a circle through two points A and B.Then $OA=OB$ because they are radius of the circle .

Hence $OAB$ is an isosceles triangle and the altitude from O to point P on $AB$ defines two congnunt triangles $OPA$ and $OPB.$

$\therefore OP$ is the perpendicular bisector of $AB.$

Any point O on the perpendicular bisector likuoise defines two congnunt triangles.such that $OA-OB$