# Circle Theorem: The Perpendicular Bisector of a Chord Passes Through the Center of the Circle (Mathematics Lesson)

# 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.

# A Real Example of the Circle Theorem that the Perpendicular Bisector of a Chord Passes Through the Center of the Circle

The slider below shows a real example of the circle theorem that the perpendicular bisector of a chord passes through the center of the circle:##### Curriculum

##### Interactive Test

**show**

##### Note

# 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.