Circle Theorem: The Perpendicular Bisector of a Chord Passes Through the Center of the Circle
Circle Theorem: The Perpendicular Bisector of a Chord Passes Through the Center of the Circle
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 that the Perpendicular Bisector of a Chord Passes Through the Center of the 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.
If a line through a chord has two of these properties, it also has the third.

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.