Question

The locus of centers of all circles passing through two given points A and B, is the perpendicular bisector the line segment AB.

• A. True
• B. False

Answer 1

The correct option is A

True

Let P and Q be the centers of two circles S and S’, each passing through two given points A and B. Then,

PA = PB [Radii of the same circle]

$\Rightarrow$ P lies on the perpendicular bisector of AB …(i)

Again, QA = QB [Radii of the same circle]

$\Rightarrow$ Q line on the perpendicular bisector of AB …(ii)

From (i) and (ii), it follows that P and Q both lie on the perpendicular bisector of AB.

Therefore, the locus of the centers of all the circles passing through A and B is the perpendicular bisector of AB.

Hence, the statement is correct.