A chord
is a segment that joins two points of the circle.
A
diameter is a chord that
contains the center of the circle. 


1.
2.
3.

In a circle, a radius
perpendicular to a chord bisects the chord.
In a circle, a radius that bisects a chord is perpendicular to
the chord.
In a circle, the perpendicular bisector of a chord passes
through the center of the circle. 

Proof of Theorem 1:
Statements 
Reasons 
1. 

1. 
Given 
2. 

2. 
Two points determine exactly one line. 
3. 

3. 
Perpendicular lines meet to form right
angles. 
4. 

4. 
A right triangle contains one right angle. 
5. 

5. 
Radii in a circle are congruent. 
6. 

6. 
Reflexive Property  A segment is congruent
to itself. 
7. 

7. 
HL  If the hypotenuse and leg of one right
triangle are congruent to the corresponding parts of another
triangle, the triangles are congruent. 
8. 

8. 
CPCTC  Corresponding parts of congruent
triangles are congruent. 
9. 
E is the midpoint of

9. 
Midpoint of a line segment is the point on
that line segment that divides the segment two congruent
segments. 
10. 

10. 
Bisector of a line segment is any line (or
subset of a line) that intersects the segment at its
midpoint. 
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. 

In a circle, or congruent
circles, congruent chords have congruent arcs.
(converse) In a
circle, or congruent circles, congruent arcs have congruent
chords. 
;

In a circle, parallel chords intercept congruent arcs. 

