The Lesson
If a line cuts through a chord of the circle, such that it crosses it at 90° and cuts it in half, that line passes through the centre of the circle.More About the Circle Theorem where the Perpendicular Bisector of a Chord Passes Through the Center of a Circle
This circle theorem deals with three properties of lines through a chord. A line that:- is perpendicular to the chord
- bisects (cuts in half) the chord
- passes through the center of the circle.
- A line that is perpendicular to a chord and bisects it must pass through the center of the circle.
- A line that is perpendicular to a chord and passes through the center of the circle must bisect the chord.
- A line that bisects a chord and passes through the center of a circle must be perpendicular to the chord.
Useful Definitions
A chord is a line whose endpoints lie on the circle.The perpendicular bisector of the chord is a line that crosses the line at 90° (perpendicular) and cuts it in half (bisector).
This perpendicular bisector of the chord passes through the center of the circle.