12-2%20Arcs%20and%20Chords

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12-2 Arcs and Chords
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Chord

• -a segment whose endpoints are on a circle.

A chord always cuts a circle into two arcs,
usually a minor and major.
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Theorem

• In the same circle, or congruent circles
• (1) Congruent central angles have congruent arcs
• (2) Congruent arcs have congruent central angles

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Theorem

• In the same circle, or congruent circles
• (1) Congruent central angles have congruent
  chords
• (2) Congruent chords have congruent central angles

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Theorem

• In the same circle or in congruent circles
• (1) Chords equally distant from the center (or
  centers) are congruent.
• (2) Congruent chords are equally distant from the
  center (or centers)

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We can have midpoints of arcs, they act just like
midpoints of segments.
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Works with radii as well.
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Find x and y.
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Find the length of a chord that is a distance of
7 inches from the center of a circle with a
radius of 11.
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is 15 and PR 9