properties of chords. when a chord intersects the circumference of a circle certain properties will...
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Properties of Chords
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When a chord intersects the circumference of a circle certain properties will be true.
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Property #1:
Chords that are equidistant from the center of a circle are equal in length.
If OE = OG , then AB = CD.
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Converse of Property #1:
Equal chords are equidistant from the center of a circle.
If AB = CD , then OE = OG.
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Property #2:
All radii of a circle are equal.
OA = OC = OD
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Property #3:A line from the center of a circle, perpendicular to a chord, bisects the chord (and the subtended arc).
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Converse of Property #3:If the line that is perpendicular to achord bisects the chord, then the line passes through the center of the circle.
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Another Converse of Property #3:If a line passing through the centerbisects a chord (or its arc), then it is perpendicular to the chord.
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Property #4
Equal chords have equal arcs.
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Converse of Property #4
Equal arcs have equal chords.
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Example
What is the distance between the two parallel chords if the radius of the circle is 7?
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Example
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Example
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Example
In a circle with radius 7 cm, a chord is 3 cm from the center. How long is another chord located 3 cm from the center?
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Example
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Example
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Example