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If a line through the center of a circle is perpendicular to a chord, then
the line bisects the chord.
If a line contains the center of a circle and the midpoint of a chord, then
the line is perpendicular to the chord
If a line is perpendicular to a chord at its midpoint, then
the lines pass through the center
In a circle or congruent circles, two chords are congruent iff they
intercept congruent arcs
In a circle, if two chords are not congruent, then the longer chord is
closer to the center
The longest chord is
the diameter
In a circle or congruent circles, two minor arcs are congruent
iff their central angles are congruent and/or the chords are equidistant from the center.
Note
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