Perpendicular bisector of any chord of a circle passes through the centre of the circle.
Draw a circle with centre at point O and radius 5 cm. Draw its chord AB, draw the perpendicular bisector of line segment AB. Does it pass through the centre of the circle ?
Draw a circle with centre C and radius 3.4 cm. Draw any chord. Construct the perpendicular bisector of and examine if it passes through C.