6.9

What More Can I Learn About Circles?

Pg. 23

Chords and Angles

What More Can I Learn About Circles? Chords and Angles

As you investigate more about the parts of a circle, look for connections you can make to other shapes and relationships you have studied so far.

B C Both intersect DA

D A Both intersect BC

~AASimilar

8 4

6x

84

= 6x

8x = 24

x = 3

6.37 – FORMULADetermine a formula that will work for any two intersecting chords.

ab = cd

ac

=db

6.38 – EXTRA PRACTICEUse the relationships in the diagrams below to solve for the variable. Justify your solution.

3x = 45

x = 15

4x = 48

x = 12

6.39 – EVENTS IN THE SKYDid you know that since 1997, over 8000 operating satellites orbited the Earth performing various functions such as taking photographs of our planet? One way scientists learn more about the Earth is to carefully examine photographs that are taken by an orbiting satellite.

a. Draw an angle from Satellite A that shows the portion of the Earth's equator that is visible from the satellite. Label the point of tangency points D and F.

D

F

b. Draw a quadrilateral ADEF that connects Satellite A, the points of tangency, and the center of the Earth (point E). What is the relationship of the sides of the angle and the circle that represents the equator of the Earth?

D

F

A

E

Right angles

c. If the measure of the angle at Satellite A is 90°, what is the measure of the degree of the equator's arc that is in plain view?

D

F

A

E

90°

90°

90°

d. What is the relationship of AD and AF? Prove that relationship using congruent triangles.

Radii in same circletangent to circle

AE = AE

AD = AF cpctcD

EF

A

HL

D

F

A

E

45°

45°4000

4000

4000 2mi

J

J

x = 22

5x – 4 = 2x + 23x – 4 = 2

3x = 6x = 2