Chapter 10 - Circles

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Chapter 10 - Circles

• Section 10.2 Arcs and Chords

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How Do You Measure a Circle or Parts of a Circle?

• Area
• Circumference
• Arc length
• Arc measure

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Unit Goal

• Use properties of arcs of circles

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Central Angles

• A central angle is an angle whose vertex is the
  center of the circle and whose sides intersect
  the circle.

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Measuring Arcs

• The measure of an arc is the same as the measure
  of its associated central angle.

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Major and Minor Arcs

• A major arc is an arc whose measure is more than
  180º.
• A minor arc is an arc whose measure is less than
  180º.
• A semicircle is an arc that measures exactly
  180º.

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Naming Minor Arcs

• Minor arcs are named by their endpoints.

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Naming Major Arcs

• Major arcs and semicircles are named by the two
  endpoints and a point on the arc.

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Example

• Find the measure of each arc

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Example

• Find the measure of each arc

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Example
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Investigate on Circle C

• Draw two distinct, congruent chords
  in circle C.
• In a different color construct the central angles
  formed by the endpoints of your chords.
• Find the measure of arc RJ and arc TK.
• What do you notice?

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Congruent Chord Theorem

• In the same circle or congruent circles, two
  minor arcs are congruent iff their corresponding
  chords are congruent.

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ExampleFind the measure of arc BD.
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More with Circle C

• Construct line through C that is perpendicular to
  
• Name the point of intersection A
• Construct line through C that is perpendicular to
  
• Name the point of intersection E
• Measure

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THEOREM

• In the same circle, or in congruent circles, two
  chords are congruent iff they are equidistant
  from the center.

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Investigate with Circle G

• Construct a diameter
• Construct a chord that is perpendicular
  to your diameter. Name the point of concurrency
  K.
• Determine the measures of

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Diameter Bisector Theorem of Congruency
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Theorem
If one chord is a perpendicular bisector of
another chord, then the first chord is a diameter.
This can be used to locate a circles center.
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Investigate on Circle E.

• Draw any two chords that are not parallel to each
  other
• Draw the perpendicular bisector of each chord.
• The perpendicular bisectors should intersect at
  the circles center.
• These are diameters.

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HW Assignment

• TB 2