10.2 Arcs and Chords

1
10.2 Arcs and Chords

• Central angle
• Minor Arc
• Major Arc

2
Central angle

• A central angle is an angle which vertex is the
  center of a circle

3
Minor Arc

• An Arc is part of the circle.
• A Minor Arc is an arc above the central angle if
  the central angle is less then 180

4
Major Arc

• A Major Arc is an arc above the central angle if
  the central angle is greater then 180

5
Semicircle

• If the central angle equals 180, then the arc is
  a semicircle.

6
Semicircle

• If the central angle equals 180, then the arc is
  a semicircle.

7
Measure of an Arc

• The measure of an Arc is the same as the central
  angle.

8
Measure of an Arc

• The measure of an Arc is the same as the central
  angle.

9
Postulate Arc Addition

• Arcs can be added together.

10
Congruent Arcs

• If arcs comes from the same or congruent circles,
  then they are congruent if then have the same
  measure.

11
Congruent chords Theorem

• In the same or congruent circles, Congruent arcs
  are above congruent chords.

                                   
                                   
12
Theorem

• If a diameter is perpendicular to a chord , then
  it bisects the chord and its arc.

13
Theorem

• If a chord is the perpendicular bisector of
  another chord (BC), then the chord is a diameter.
  

14
Solve for y

15
Solve for y

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Theorem

• In the same or congruent circles, two chords are
  congruent if and only if they are an equal
  distance from the center.

17
Solve for x, QT

• UV 6 RS 3 ST 3

18
Solve for x, QT

• UV 6 RS 3 ST 3
• x 4,
• Since Congruent
• chord are an
• equal distance
• from the center.

19
Solve for x, QT

• UV 6 RS 3 ST 3
• x 4,

20
Find the measure of the arc

• Solve for x and y

21
Find the measure of the arc

• Solve for x and y

22
Homework

• Page 607 608
• 12 - 38

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Homework

• Page 608 -609
• 39 47,
• 49 51,
• 69, 76 - 79