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A chord is a segment that joins two points of a circle. |
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A diameter is a chord that contains the center of the circle. |
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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. |
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Proof:
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Proof of the converse is left as an exercise.
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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. |
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Proof:
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Proof of the converse is left as an exercise.
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In a circle, or congruent circles, congruent chords have congruent arcs. |
Converse: |
In a circle, or congruent circles, congruent arcs have congruent chords. |
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Proof:
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Proof of the converse is left as an exercise.
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In a circle, parallel chords intercept congruent arcs |
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Proof:
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