Introduction to Circles

1
Lesson 10-1

• Introduction to Circles

2
Circles - Terms
Circumference
90
Diameter (d)
Radius (r)
0
180
Center
Chord
270
Circumference 2pr dp
3
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 2pr or C dp

4
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

5
Example 1-1a
a. Name the circle.
b. Name the radius of the circle.
c. Name a chord of the circle.
d. Name a diameter of the circle.
6
Example 1-1e
7
Example 1-2a
a. If ST 18, find RS.
Formula for radius
Substitute and simplify.
Answer 9
b. If RM 24, find QM.
Formula for diameter
Substitute and simplify.
Answer 48
c. If RN 2, find RP.
Answer So, RP 2.
Since all radii are congruent, RN RP.
8
Example 1-2d
Answer 12.5
Answer 58
Answer 8.5
9
Example 1-3a
Find EZ.
10
Example 1-3b
Segment Addition Postulate
Substitution
Simplify.
Answer 27 mm
11
Example 1-3c
Find XF.
Answer 11 mm
12
Example 1-3e
Answer 6.5 in.
Answer 13.5 in.
13
Example 1-4a
a. Find C if r 13 inches.
Circumference formula
Substitution
b. Find C if d 6 millimeters.
Circumference formula
Substitution
14
Example 1-4c
Find d and r to the nearest hundredth if C 65.4
feet.
Circumference formula
Substitution
Use a calculator.
Radius formula
Use a calculator.
15
Example 1-4e
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.
16
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 pd
  or C 2pr
• Homework pg 526-527 16-20, 32, 33,
  44-47