When you’re working with a circle, there are five important theorems that you need to know about the properties of the circle’s radii and chords. (There are really just three ideas; but two of the theorems work in both directions which brings the total to five):
Segment PG is a chord, segment AB is the diameter, and segment OC is the radius of this circle.
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Radii size: All radii of a circle are congruent.
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Perpendicularity and bisected chords:
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If a radius is perpendicular to a chord, then it bisects the chord.
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If a radius bisects a chord (that isn’t a diameter), then it’s perpendicular to the chord.
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Distance and chord size:
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If two chords of a circle are equidistant from the center of the circle, then they’re congruent.
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If two chords of a circle are congruent, then they’re equidistant from its center.
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