1. 11-2 Arcs and chords
Geometry

2. Central angle
Central angle- angle whose vertex is the center of a circle A
ACB is a central angle C B

3. Arcs A Arc- a piece of a circle. Named with 2 or 3 letters
Measured in degrees
Minor arc- part of a circle that measures less than 180o (named by 2 letters). B B ( BP P

4. More arcs
Major arc- part of a circle that measures between 180o and 360o.
(needs three letters to name)
Semicircle- an arc whose endpts are the endpts of a diameter of the circle
(OR ½ of a circle) A B ( (
ABC or CBA C C S

5. Arc measures Measure of a minor arc- measure of its central 
Measure of a major arc- 360o minus measure of minor arc

6. Ex 1: find the arc measures(
50o
m AB= ____
m BC= ____
m AEC= ____
m BCA= _____ (
130o ( A
180o
180o D (
180o+130o = 310o
50o
130o C
50, 130, 180, 310
OR 360o- 50o = 310o B

7. Post. 26 arc addition postulate
The measure of an arc formed by two adjacent arcs is the sum of the measures of those arcs. B A ( ( ( C
m ABC = m AB+ m BC

8. Congruency among arcs Congruent arcs- 2 arcs with the same measure
MUST be from the same circle OR  circles!!!

9. Example 2 (
m AB=___ A (
m DC=____ E
30o B D ( (
30o DC
30, 30, C

10. Ex 3: ( ( ( ( m BD= 45o A m AE= 45o B BD @ AE
The arcs are the same measure; so, why aren’t they ?
45o C D E
The 2 circles are NOT  !

11. Thm 10.4
In the same circle (or circles), 2 minor arcs iff their corresponding chords A ( (
BC iff BC B C

12. Thm 10.5
If a diameter of a circle is  to a chord, then the diameter bisects the chord and its arc.
If EG is  to DF, then CF and GF ( ( E C D F G

13. Thm 10.6
If one chord is a  bisector of another chord then the 1st chord is a diameter. M
If JK is a  bisector of ML, then JK is a diameter. K J L

14. Ex 4: find m BC ( ( ( B By thm 10.4 BD @ BC. 3x+11 3x+11=2x+47 2x+47
2(36)+47
72+47 A
X = 36, 119 degrees
119o D C

15. Thm10.7
In the same circle (or in  circles), 2 chords are  iff they are =dist from the center. D C
CB iff AF G F A E B

16. Ex 5: find CG. B CF @ CG 72=CF2+62 6 G 49=CF2+36 6 13=CF2 A CF = ð13 C

17. Assignment