Lesson 10-1

Introduction to Circles

Circles - Termsy

x

Chord

Radius (r)

Diameter (d)

Center

Circumference = 2πr = dπ

0°180°

90°

270°

Objectives

• Identify and use parts of circles– circle– center– radii, r– chords– diameter (2r = d): longest chord

• Solve problems involving the circumference of a circle– formulas: C = 2πr or C = dπ

Vocabulary

• Circle – the locus (set) of all points in a plane equidistant for a given point

• Center – the central point of a circle• Chord – any segment that endpoints are on

the circle• Diameter – a chord that passes through the

center of the circle• Radius – any segment that endpoints are the

center and a point on the circle• Circumference – perimeter of a circle

a. Name the circle.

Answer: The circle has its center at E, so it is named circle E, or .

Answer: Four radii are shown: .

b. Name the radius of the circle.

Answer: Four chords are shown: .

c. Name a chord of the circle.

d. Name a diameter of the circle.

Answer: are the only chords that go through the center. So, are diameters.

Answer:

Answer:

a. Name the circle.

b. Name a radius of the circle.

c. Name a chord of the circle.

d. Name a diameter of the circle.

Answer:

Answer:

EXAMPLE 2

Answer: 9

Formula for radius

Substitute and simplify.

a. If ST = 18, find RS.Circle R has diameters and .

Answer: 48

Formula for diameter

Substitute and simplify.

b. If RM = 24, find QM.

c. If RN = 2, find RP.

Answer: So, RP = 2.Since all radii are congruent, RN = RP.

EXAMPLE 3

Answer: 58

Answer: 12.5

a. If BG = 25, find MG.

b. If DM = 29, find DN.

Circle M has diameters

c. If MF = 8.5, find MG.

Answer: 8.5

EXAMPLE 4

Find EZ.

The diameters of and are 22 millimeters, 16 millimeters, and 10 millimeters, respectively.

EXAMPLE 5

Since the diameter of FZ = 5.

Since the diameter of , EF = 22.

Segment Addition Postulate

Substitution

is part of .

Simplify.

Answer: 27 mm

(CONT)

Find XF.

The diameters of and are 22 millimeters, 16 millimeters, and 10 millimeters, respectively.

Answer: 11 mm

Since the diameter of , EF = 22.

is part of . Since is a radius of

EXAMPLE 6

The diameters of , and are 5 inches, 9 inches, and 18 inches respectively.

a. Find AC.

b. Find EB.

Answer: 6.5 in.

Answer: 13.5 in.

EXAMPLE 7

a. Find C if r = 13 inches.

Circumference formula

Substitution

Answer:

b. Find C if d = 6 millimeters.

Circumference formula

Substitution

Answer:

EXAMPLE 8

Find d and r to the nearest hundredth if C = 65.4 feet.

Circumference formula

Substitution

Use a calculator.

Divide each side by .

Radius formula

Use a calculator.

Answer:

EXAMPLE 9

a. Find C if r = 22 centimeters.

b. Find C if d = 3 feet.

c. Find d and r to the nearest hundredth if C = 16.8 meters.

Answer:

Answer:

Answer:

EXAMPLE 10

Summary & Homework

• Summary:– Diameter of a circle is twice the radius– Circumference, C, of a circle with diameter,

d, or a radius, r, can be written in the form C = πd or C = 2πr

• Homework: pg 526-527; 16-20, 32-35, 44-47