

A chord is a segment that joins two points of a circle. 


A diameter is a chord that contains the center of the circle. 


In a circle, a radius perpendicular to a chord bisects the chord. 
Converse: 
In a circle, a radius that bisects a chord is perpendicular to the chord. 
Also stated: 
In a circle, the perpendicular bisector of a chord passes through the center of the circle 
Extended form: 
In a circle, a diameter perpendicular to a chord bisects the chord and its arc. 




Proof:


Proof of the converse is left as an exercise.

In a circle, or congruent circles, congruent chords are equidistant from the center. 
Converse: 
In a circle, or congruent circles, chords equidistant from the center are congruent. 




Proof:


Proof of the converse is left as an exercise.

In a circle, or congruent circles, congruent chords have congruent arcs. 
Converse: 
In a circle, or congruent circles, congruent arcs have congruent chords. 




Proof:


Proof of the converse is left as an exercise.

In a circle, parallel chords intercept congruent arcs 




Proof:


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