Vocab reminder: a chord is a segment with endpoints on a circle.
Properties of Chords:
*any chord divides a circle into 2 arcs.
*A diameter divides the circle into 2 semicircles.
*Any other chord divides a circle into a minor arc and a major arc.
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Chord Theorems
Theorem #1: 2 minor arcs are congruent if and only if their
corresponding chords are congruent.
Example 1
Example 2
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Theorem #2: if one chord is a perpendicular bisector of another
chord, then the first chord is a diameter.
Theorem #3: if a diameter of a circle is perpendicular to a chord,
then the diameter bisects the chord and its arc.
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Example 4:
Find the length of BD.
Example 3:
Find the length of BF.
Example 5: Find the measure of the
following arcs.
a)
b)
c)
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Theorem #4: 2 chords are congruent if and only if they are
equidistant from the center.
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Example 6: Find AQ.
Example 7:
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Now, on your own...
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