Transcript Lesson 1 Contents

Lesson 10-1
Introduction to Circles
Circles - Terms
y
90°
180°
Radius (r)
Center
Chord
270°
Circumference = 2πr = dπ
x
0°
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
.
b. Name the radius of the circle.
Answer: Four radii are shown:
.
c. Name a chord of the circle.
Answer: Four chords are shown:
.
d. Name a diameter of the circle.
Answer:
are the only chords that go through
the center. So,
are diameters.
a. Name the circle.
Answer:
b. Name a radius of the circle.
Answer:
c. Name a chord of the circle.
Answer:
d. Name a diameter of the circle.
Answer:
Circle R has diameters
a. If ST = 18, find RS.
and
.
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.
Since all radii are congruent, RN = RP. Answer: So, RP = 2.
Circle M has diameters
a. If BG = 25, find MG.
Answer: 12.5
b. If DM = 29, find DN.
Answer: 58
c. If MF = 8.5, find MG.
Answer: 8.5
The diameters of
and
are 22 millimeters,
16 millimeters, and 10 millimeters, respectively.
Find EZ.
Since the diameter of
, EF = 22.
Since the diameter of
FZ = 5.
is part of
.
Segment Addition Postulate
Substitution
Simplify.
Answer: 27 mm
The diameters of
and
are 22 millimeters,
16 millimeters, and 10 millimeters, respectively.
Find XF.
Since the diameter of
is part of
. Since
Answer: 11 mm
, EF = 22.
is a radius of
The diameters of
, and
are 5 inches,
9 inches, and 18 inches respectively.
a. Find AC.
Answer: 6.5 in.
b. Find EB.
Answer: 13.5 in.
a. Find C if r = 13 inches.
Circumference formula
Substitution
Answer:
b. Find C if d = 6 millimeters.
Circumference formula
Substitution
Answer:
Find d and r to the nearest hundredth if C = 65.4 feet.
Circumference formula
Substitution
Divide each side by .
Use a calculator.
Radius formula
Use a calculator.
Answer:
a. Find C if r = 22 centimeters.
Answer:
b. Find C if d = 3 feet.
Answer:
c. Find d and r to the nearest hundredth if C = 16.8 meters.
Answer:
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, 33, 44-47