Arcs of a Circle

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Arcs of a Circle
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The Circle and their Arcs

• ARC
• An arc consists of two points on a circle and all
  of the points on the circle needed to connect the
  points by a single path

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The Circle and their Arcs

• Center of an ARC
• The center of an arc is the center of the circle
  of which the arc is a part.

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The Circle and their Arcs

• Central Angle
• A central angle is an angle whose vertex is at
  the center of a circle.
• The measure of a central angle is equal to the
  measure of its intercepted arc!

63 degrees
131 degrees
?
Note the measure of a central angle is less
than 180 degrees
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The Circle and their Arcs

• Minor ARC
• A minor arc is an arc whose points are on or
  between the sides of a central angle
• The measure of a minor arc is always less than
  180 degrees

A minor arc is named with its endpoints.
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The Circle and their Arcs

• Major ARC
• A major arc is an arc whose points are outside
  the sides of a central angle
• The measure of a major arc is always greater than
  180 degrees

A major arc must be named with three points on
the circle!
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The Circle and their Arcs

• Semicircle
• A semicircle is an arc whose endpoints are on the
  diameter of a circle
• The measure of a semicircle is always equal to
  180 degrees

A semicircle must be named with three points on
the circle!
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The Circle and their Arcs

• Measure of a Minor ARC
• The measure of a minor arc is equal to the
  measure of its central angle
• The measure of a minor arc is always less than
  180 degrees

The measure of the minor arc
is indicated by
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The Circle and their Arcs

• Measure of a Major ARC
• The measure of a major arc is equal to the 360
  minus the measure of its central angle
• The measure of a minor arc is always more than
  180 degrees

The measure of the major arc
is indicated by
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The Circle and their Arcs

• Congruent Arcs
• Two arcs are congruent whenever they have the
  same measure and are parts of the same circle or
  congruent circles.

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The Circle and their Arcs

• Arcs with the same measure that are NOT Congruent
  Arcs

3cm
5 cm
Arcs are not in the same or congruent circles!