Question

The centre of a circle always lies on the perpendicular bisector of any given chord.

• A. True
• B. False

Answer 1

The correct option is A True

Consider a line segment AB, point "C" is a point on the perpendicular bisector of AB. Triangle ABC is a isosceles triangle as AC = BC. We can say that all the points that form a isosceles triangle are on the perpendicular bisector. Now consider a circle with centre "O" and chord EF, OE = OF (radii). This implies OEF is a isosceles triangle. So, point "O" always lies on the perpendicular bisector.