Transcript Circle - BakerMath.org
10.1 Circles and Circumference
Objectives
Identify and use parts of circles Solve problems using the circumference of circles
Parts of Circles
Circle
– set of all points in a plane that are
equidistant
from a given point called the
center
of the circle.
A circle with center P is called “circle P” or
P
.
P
Parts of Circles
The distance from the center to a point on the circle is called the
radius
of the circle. The distance across the circle through its center is the
diameter
circle. The diameter is twice the radius of the
d = 2r
or
r = ½ d
).
The terms
diameter
measures.
radius
and describe segments as well as
Parts of Circles
QP , QS , and QR are radii.
All radii for the same circle are congruent.
PR is a diameter .
All diameters for the same circle are congruent.
A
chord
endpoints are points on the circle. PS is a segment whose and PR are chords.
A diameter is a chord that passes through the center of the circle.
Example 1a:
Name the circle.
Answer:
The circle has its center at
E,
circle
E,
or . so it is named
Example 1b:
Name the radius of the circle.
Answer:
Four radii are shown: .
Example 1c:
Name a chord of the circle.
Answer:
Four chords are shown: .
Example 1d:
Name a diameter of the circle.
Answer:
are the only chords that go through the center. So, are diameters.
Your Turn:
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:
Example 2a:
Circle R has diameters and . If ST 18 , find RS. Formula for radius Substitute and simplify.
Answer:
9
Example 2b:
Circle R has diameters . If RM 24 , find QM. Formula for diameter Substitute and simplify.
Answer:
48
Example 2c:
Circle R has diameters . If RN 2 , find RP. Since all radii are congruent,
RN
=
RP.
Answer:
So,
RP
= 2.
Your Turn:
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
Example 3a:
The diameters of and are
22
millimeters, 16 millimeters, and 10 millimeters, respectively.
Find EZ.
Example 3a:
Since the diameter of ,
EF
= 22.
Since the diameter of
FZ
= 5.
is part of .
Segment Addition Postulate Substitution Simplify.
Answer:
27 mm
Example 3b:
The diameters of and are
22
millimeters, 16 millimeters, and 10 millimeters, respectively.
Find XF.
Example 3b:
Since the diameter of ,
EF
= 22.
is part of . Since is a radius of
Answer:
11 mm
Your Turn:
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.
Circumference
The
circumference
of a circle is the distance around the circle. In a circle,
C = 2πr or πd
Example 4a:
Find C if r = 13
inches.
Circumference formula Substitution
Answer:
Example 4b:
Find C if d = 6
millimeters.
Circumference formula Substitution
Answer:
Example 4c:
Find d and r to the nearest hundredth if C = 65.4
feet.
Circumference formula Substitution Divide each side by .
Use a calculator.
Example 4c:
Radius formula Use a calculator.
Answer:
Your Turn:
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:
Example 5:
MULTIPLE- CHOICE TEST ITEM Find the exact circumference of . A B C D Read the Test Item
You are given a figure that involves a right triangle and a circle. You are asked to find the exact circumference of the circle.
Example 5:
Solve the Test Item
The radius of the circle is the same length as either leg of the triangle. The legs of the triangle have equal length. Call the length
x
.
Pythagorean Theorem Substitution Simplify.
Divide each side by 2.
Take the square root of each side.
Example 5:
So the radius of the circle is 3.
Circumference formula Substitution Because we want the exact circumference, the answer is B.
Answer:
B
Your Turn:
Find the exact circumference of . A B C D Answer:
C
Assignment
Geometry
Pg. 526 #16 – 42, 44 – 54 evens
Pre-AP Geometry
Pg. 526 #16 - 56