Chapter 7 – Circles In previous chapters, you have extensively studied triangles and quadrilaterals to learn more about their sides and angles. In this chapter, you will connect your understanding of polygons with your knowledge of the area ratios of similar figures to find the area and circumference of circles of all sizes. You will explore the relationships between angles, arcs, and chords in a circle. Then you will find the equation of a circle using the Pythagorean Theorem.

7.1

What If There Are No Sides?

Pg. 4Circumference and Arc Length

7.1 – What If There Are No Sides?Circumference and Arc Length

In previous chapters you discovered the perimeter and area of polygons. Today you will discover how to find the perimeter of a shape with no sides, a circle.

Term Definition Picture

Circle

The set of all points in a plane that are equidistant from a given point

Term Definition Picture

Center

Point equidistant from the sides of the circle. Gives the name of the circle.

P

P

Term Definition Picture

Radius

A segment with endpoints at the center and on the circle

P

PQ

Q

Term Definition Picture

Diameter

A segment with both endpoints on the circle that goes through the center of the circle

P

QR

Q

R

diameter = 2 radius

7.1 – RATIOS OF CIRCLESFind the measure of the circumference by wrapping a string around the entire perimeter of the circle and then measuring how long the string is in centimeters. Then estimate the diameter (length across the circle). Then write the ratio. What do you notice? What value are you finding?

Circumference Length around a circle

C d

C =2 r

7.3 – MISSING INFORMATIONUsing your understanding of the relationship between circumference (perimeter of a circle) and the diameter, find the missing values. a. Find the circumference of a circle with a diameter of 12 inches.

C d3.14 12C 37.68C in

C d22 d

22 yd d

c. Find the circumference of a circle with a radius of 16 inches. Leave answers in terms of pi.

2C r 2 16C

32C in

d. Michael noticed a pattern in the relationship between the radius, diameter, and circumference. Complete the table below. Be sure to leave pi in your answer when finding the circumference.

3

6

5

10 24

24

10

2015

302r

2r

7.4 – WHEELS GO ROUND AND ROUNDEvelyn's in-line skate wheels have a 0.42m diameter. How many meters will Evelyn travel after 5000 revolutions of the wheels on her in-line skates?

C d

2100 m0.42C 5000

6597.34m

7.5 – PERIMETERFind the perimeter of each shape. Leave answers in terms of pi.

C d300C

329658 m

2C r 2 5C 10C 2

5

10

10

10 5

30 mm

ArcPart of a circle

AC ABC

Arc Length: Length around part of a circle

2

x

r

degree of arc

360

7.6 – ARC LENGTHFind the part of the circumference that is between points A and B.

90

360 2 7

x

360x 1260

3.5x in

45

360 2 12

x

360x 1080

3x cm

120

360 2 6

x

360x 1440

x 4 ft

7.7 – ARC LENGTHFind the length of the shaded arc. Leave answers in terms of pi.

315315

360 2 20

x

360x 12600

35x m

300300

360 2 9

x

360x 5400

15x in

http://www.youtube.com/watch?v=GmiXemW_oBQ