circles and the points, segments, lines related to it

THE CIRCLE and the

Geometric Figures Related

to ItPoints

Segments

Lines

PICTURE! PICTURE!

Bangui Windmills

by Agnes Manalofrom Google Images

G

O

D

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•

•

LEO The Lionby stylecraze

from Google Images

V

L

E

S

O

Ziplinefrom Google Images

Y

u

O

DEFINITION

A

Note: A circle is named by its center. The circle above is named circle A or .

A circle is the set of all points in a plane that are the same distance from a given point, called the center of a circle.

Using circle A,1. Draw the following points:a. L inside circle A; b. G outside circle A; c. N, I, C, and E on circle A.

LET’S EXPLORE!

POINTS

A

L

Interior points

A

G

AI

E

Exterior points

Points on the circle

C

N

Using circle A,2. Connect the following points:

a. A and I; b. C and N; c. E and C.

LET’S EXPLORE!

SEGMENTS

A

I

diameterchordradiusC

ANA

E

C

A of

radius a is AI

A of

chord a is NC

A of

diameter a is EC

RadiusLine segment whose endpoints are the center of a circle and any point on the circle

Definition:

Chord

Line segment whose endpoints are any two points on a circle

Definition:

DiameterLine segment that passesthrough the center of a circle, and whose endpoints lie on the circle

Definition:

3. Compare the measures of the segments AI, AE and AC.4. How is the measure of segment EC related to themeasures of segments AI, AE, and AC?

LET’S EXPLORE!

SEGMENTS

A

I

diameterchordradiusC

ANA

E

C

A of

radius a is AI

A of

chord a is NC

A of

diameter a is EC

Note: All radii of the same circle are congruent.The diameter is twice the radius.The diameter is the longest chord in a circle.

Using circle A,3. Draw a line containing the points:

a. E and G; b. I and C;

LET’S EXPLORE!

LINES

G

E

secanttangentC

I

A of

secant a is IC

A of

tangenta is EG

AA

Tangent• A line is tangent to

the circle if it touches it just once. Such a line is called a tangent or a tangent line. The point where the tangent touches the circle is called the point of tangency.

• We can also speak of tangent segments or rays.

Definition:

Secant• A line that intersects

the circle twice is called a secant line or a secant.

• Line segments and rays may also be secants.

• Often, secants are drawn from a point outside of the circle to a point on the circle.

Definition:

Identify each of the following as related to ʘ A.1. A2. RP3. PI4. SR5. IS6. PE7. AR8. SI9. AS10. P

Name each of the following:

1. a circle 2. one interior point3. four exterior points4. four points on the circle 5. center 6. two points of tangency 7. four radii8. a chord9. two diameters10. two tangents11. a secant

Work in pairs and try this!Using the circle at the right, A. Draw: (1) radius HJ; (2) diameter IC; (3) chord IS; (4) a line passing through points H and R; (5) line ST

Work in pairs and try this!Using the circle at the right, B. Connect the points: (6) T and C; (7) C and H (8) H and I

Work in pairs and try this!

Using the circle at the right, C. Name the following: (9) a circle; (10) an exterior point (11) a tangent line (12) a secant line (13) a point of tangency (14 - 16) three radii (17 - 20) four chords (aside from IS or SI)

Answers:

S

CJ

I

H R

T

9. J10. R11. HR or RH12. TS or ST13. H14 -16. HJ or JH IJ or JI CJ or JC17 - 20

HI or IHCT or TCCH or HCST or TS

SEGMENTS

A

I

diameterchordradiusC

ANA

E

C

A of

radius a is AI

A of

chord a is NC

A of

diameter a is EC

LINES

G

E

secanttangentC

I

A of

secant a is IC

A of

tangenta is EG

AA

THE CIRCLE and the

Geometric Figures Related

to ItPoints

Segments Lines

THE CIRCLE and the

Geometric Figures Related

to ItPoints

Segments

THE CIRCLE and the

Geometric Figures Related

to ItPoints