252.5

158.4

107.3

12.2

145.1

2

2

2

2

2

xx

xx

xx

xx

xx

Factor Warm – up Session 28 27 xx

43 xx

25 xx

35 xx

212 xx

Math IIDay 28 (9-17-09)

UNIT QUESTION: What special properties are found with the parts of a circle?Standard: MM2G1, MM2G2

Today’s Question:What are the parts of a circle?Standard: MM2G3.a,d

AGENDA1. Notes 6.1 - Circles2. Class Work3. Home Work

Friday 9/17

6.2

Parts of a Circle

Circle – set of all points _________ from a given point called the _____ of the circle.

C

Symbol:

equidistant

center

C

CHORD: a segment whose ________ are on the circle

endpoints

P

RADIUS: distance from the _____ to a point on the circle

center

Radius

Diameter

P

DIAMETER: distance ______ the circle through its ______

center

across

Also known as the longest chord.

What is the relationship between the diameter and the radius of a circle?

r =

OR

D =

½ D

2 r

D = ?

r = ?

r = ? D = ?

Use P to determine whether each statement is true or false.

P

Q

R

TS

diameter. a is .1 RT False

radius. a is .2 PS True

chord. a is .3 QT True

Secant Line

A secant line intersects the circle at exactly TWO points.

TANGENT: a LINE that intersects the circle exactly ONE

time

Point of Tangenc

y

Name the term that best describes the line.

Secant

Radius

DiameterChord

Tangent

Two circles can intersect…

•in two points

•one point

•or no points

No points of intersection (different center)

No points of intersection (same center)

Same center but different radii

1 point of intersection(Tangent Circles)

Internally Tangent

Externally Tangent

2 points of intersection

INTERIOR

A point is inside a circle if its distance from the center is less than the radius.

EXTERIOR

A point is outside a circle if its distance from the center is greater than the radius.

A point is on a circle if its distance from the center is equal to the radius.

If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

Point of Tangenc

y

More Pythagorean Theorem type problems! Yeah!!

a2 + b2 = c2

x = 15

92 + 122 = x2

a2 + b2 = c2

RQ = 16

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

122 + (QR)2 = 202

r2 + 242 = (r + 16)2

r = 10

r2 + 576 = r2 + 32r + 256320 = 32r

R

S

T

TSRS If two segments from

the same exterior point are tangent to a circle, then they are

congruent.

Party hat problems!

R

S

T

22 x

11 1122 x92 x

3 3 xorx

A

C

B152 x

x14

15x

AC

E

3

4

7X

B

D

X

P

TS

Q10 4

18NP

P

N

R

12