The Perpendicular Bisector of a Chord

A chord is a line segment that passes through a circle joining any 2 points that touches the circumference of a circle. When a chord is drawn through the centre of the circle, it divides the circle into two identical parts called the semi-circle.

When there is a perpendicular bisector CD of the line segment AB, it is a line segment perpendicular to AB that passes through the midpoint M.

The perpendicular bisector of a line segment can be constructed by drawing a line segment perpendicular which passes through the centre, perpendicular to an existing line segment. The green line segment SR is the existing line segment while the green line AO is the perpendicular bisector of the line segment SR. Point O is the centre of the circle and angle SAO is a right-angle. Thus, line AO is perpendicular to line SR, making it a perpendicular bisector.

One of the various applications using Perpendicular bisector of a chord in real-life is to locate the centre of a circular structure or object. For example, the singapore flyer. Have you wondered how did the architects find the exact centre of such a huge circular stucture? Now you know that they could have used the Perpendicular bisectors of the Singapore Flyer's cords to find the flyer's axis. The multiple perpendicular bisectors

crisscrossing one another will show the centre of the flyer where the perpendicular bisectors meet.

Done by Benedict Tan