Geometry Circles

8/7/2019 Geometry Circles

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Parts of a Circle

Circle

set of allpoints _________from a given pointcalled the _____of the circle.

C

Symbol:

equidistantcenter

C


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Parts of a Circle

centerF

Use the center to name a circle.

Circle F

F


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Parts of a Circle

Segments & Lines

chord

diameter

radius

tangent

secant


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P

RADIUS:distance fromthe _____ toa point on thecircle

center

Radius


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Diameter

P

DIAMETER:distance

______ thecircle through

its ______enteracross

Also known as thelongest chord.


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Formulas

Radius/diameter

Circumference

radius = diameter

r = d

diameter = 2(radius)

d = 2r

C = 2r or C = d


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What is the relationship between the

diameter and the radius of a circle?

r=

OR

D =

D

2 r


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CHORD: asegment whose

________ areon the circleendpoints


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Secant Line

A secant lineintersects thecircle atexactly TWOpoints.


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TANGENT: a LINEthat intersects the

circle exactly ONE time


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If a line (segment or ray) is tangent to acircle, then it is perpendicular to the radius

drawn to the point of tangency.

Point ofTangency

More Pythagorean Theorem type problems!

Yeah!!


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Name the term that best describes the line.


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Types of Angles

Central angle

- Vertex is on the center.

Inscribed angle- Vertex is on the circle.


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Types of Arcs

P

M

O

major arc

minor arc

semicircle N

MO

MNO

MON


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Measure of Arcs & Angles

minor arc = its central angle

major arc = 360 - its central angle

68

68

36068 = 292

292


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semicircle = 180

180


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semicircle = 180

inscribed angle= minor arc

68

34


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Arc and Chord Relationships

If chords are

congruent,

then arcs are

congruent.

A

B

C

D

CDAB then AB

CD


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If a diameter is

perpendicular

to a chord, then

it bisects the

chord.

A

B

K

KBAKABGH

G H


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If a diameter is

perpendicular

to a chord, then

it bisects the

arc.

A

B

K

ABGH

G H

AH BH


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Two chords are

if and only if

they are the

same distance

from the center.

A

B

C

D

P O

R

PRPOCDAB


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D = ?

r = ?

r = ?

D = ?

U P d h h h


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UseP to determine whether each

statement is trueor false.

P

Q

R

T S

False

True

True


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Two circles can intersect

in two points

one point

or no points


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2 points of intersection


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1 point of intersection

(Tangent Circles)

InternallyTangent

ExternallyTangent


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No points of intersection (same center)

Same centerbut different

radii

No points of intersection


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No points of intersection

(different center)


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a2 + b2 = c2

x = 15

92 + 122 = x2


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a2 + b2 = c2

RQ = 16

122 + (QR)2 = (8+12)2

122 + (QR)2 = 202

r2 + 242 (r + 16)2


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r2 + 242 = (r + 16)2

r = 10

r2 + 576 = r2 + 32r + 256

320 = 32r

S


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R

S

T

If two segments fromthe same exterior point

are tangent to a circle,then they are congruent.

Party hatproblems!


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R

S

T

33 xorx


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A

C

B

15x


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AC

E

7X

B

D

P


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T S

Q

18NP

P

N

R


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(H, K) IS THE CENTERR IS THE RADIUS

EQUATION OF A

CIRCLE:

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