WARM UPFind the following measures.

1)

2)

3)

4)

5)

mBD

m COD

mCB

m CAD

mADC

49

68

OA B

D

C

Section 9.4Relationships between

Arcs and Chords

CHORDS

• Remember diameters are also

chords.

• By definition a chord is a segment

that has two end points on the

circle.

CHORDS and ARCS

• What is true about chords and the arcs they make?

• What is x?

Congruent chords make congruent arcs

10

10

158o

xo

158o

ARCS and CHORDS• What happens if you know the arcs?

• What is y?

Congruent arcs make congruent chords

y

16.5 142.87o

142.87o

16.5

Diameters and Chords• A diameter that is perpendicular to a

chord bisects the chord and its arc.

Find the measure of

x and the measure

of each arc.

x

12.5

127o

12.5

63.5o

63.5o

116.5o

116.5o

Same circles or Congruent circles

• Congruent chords are equally distant from the center

x

11

4

y

x = 4

y = 11

Find the missing values.

yx

13

5

zz = 13 – 5 because it’s a radius

z = 8

z = 8

13

y = 12 because its equal to x.

x = 12 because it’s a Pythagorean Triple.

z

606 y

x

o

o

Find the missing values.

3 3

60o

30o

60o

30o

6

Use a 30-60-90 triangle to solve for the missing legs.

3

= 3

3 3

60o 60o

120o

Find the missing values.

z

105

x

y

8

o

o105o

8

16

QUIZ

9.1 Circle Terms

9.2 Tangents

9.3 Arcs and Central Angles

9.4 Chords and Arcs

Practice Problems

• Page 346

• Classroom Exercises

• #4, 5

• Page 347

• Written Exercises #10 – 13