1. Section 10.2 – Arcs and Chords
Chapter 10 - Circles
Section 10.2 – Arcs and Chords

2. How Do You Measure a Circle or Parts of a Circle?
Area
Circumference
Arc length
Arc measure

3. Central Angles
A central angle is an angle whose vertex is the center of the circle and whose sides intersect the circle. A P B
is a central angle

4. Measuring Arcs
The measure of an arc is the same as the measure of its associated central angle. A P B

5. 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.

6. Naming Minor Arcs
Minor arcs are named by their endpoints.
Arc

7. Naming Major Arcs
Major arcs and semicircles are named by the two endpoints and a point on the arc.
Arc

8. Example
Find the measure of each arc: a.
70º b. c.

9. Example
Find the measure of each arc:
90º
40º
60º a. b. c.

10. Example
Find x and :

11. 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?

12. Congruent Chord Theorem
In the same circle or congruent circles, two minor arcs are congruent iff their corresponding chords are congruent.

13. Example Find the measure of arc BD.

14. More with Circle C Construct line through C that is perpendicular to
Name the point of intersection A
Name the point of intersection E
Measure

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

16. 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

17. Diameter Bisector Theorem of Congruency

18. 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 circle’s center.

19. 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.