Arcs and Chords

1
Lesson 10.2

• Arcs and Chords

2
Arcs of Circles

• Central Angle-angle whose vertex is the center of
  the circle.

3
Minor Arc

• formed from a central angle less than 180

4
Major Arc

• formed from a central angle that measures between
  180 - 360

5
Semicircle

• formed from an arc of 180
• Half circle!
• Endpoints of an arc are endpoints of the diameter

6
Naming Arcs

• How do we name minor arcs, major arcs, and
  semicircles??

7
Minor Arc

• Named by the endpoints of the arc.

8
Major Arc

• Named by the endpoints of the arc and one point
  in between the arc

9
Semicircle

• Named by the endpoints of the diameter and one
  point in between the arc

10
Example
11
Measuring Arcs

• A Circle measures 360

12
Measure of a Minor Arc

• Measure of its central angle

13
Measure of a Major Arc

• difference between 360 and measure of minor arc

14
Arc Addition Postulate

• Measure of an arc formed by two adjacent arcs is
  the sum of the measures of the two arcs.

15
Example for 1-10
16
Congruent Arcs

• Two arcs of the same circle or congruent circles
  are congruent arcs if they have the same measure.

17
Theorem 10.4

• Two minor arcs are congruent iff their
  corresponding chords are congruent.

Chords are congruent
18
Example 1Solve for x
2x
X40
19
Theorem 10.5

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

20
Example. Find DC.
21
Theorem 10.6

• If one chord is a perpendicular bisector to
  another chord, then the first chord is a diameter.

22
Example. Solve for x.
x 7
23
Theorem 10.7

• Two chords are congruent iff they are equidistant
  from the center.

Congruent Chords
24
Example. Solve for x.
x 15