Circles
Ms. Le’s Geometry Unit,
Lesson 1
Warm Up
Get into group of 2 and answer the following:
1. What does a circle means?
1. How does a circle related to math?
1. How are circles utilized in real life? (provide 3 examples)
Warm Up
How are circles utilized in real life? Examples
1.
Clock
Pizza
Softball
Bike
Earth
Objectives
• Students will be able to recognize and define a circle and it's parts:
radius, diameter, chords, central angle, major and minor arcs and
adjacent arcs.
• Student will be able to find the center of a circle and compute the
radius.
• Students will be able to recognize the relationships that the
different arcs have to the circle and to one another.
Definitions
• A circle is the set of all points in a plane that are
the same distance from a fixed point called the
center of the circle.
radius
• A radius of a circle is a line segment extending
from the center to the circle.
center
• A diameter is a line segment that joins two points
on the circle and passes through the center.
diameter
5
Naming a Circle
• A circle in a diagram is named by its center.
The circle at right is called circle O or:
• If there is more than one circle in a
diagram with the same center, this
notation does not suffice.
O
• Note: two circles in the same plane with
the same center are called concentric
circles.
6
The outside of the circle is called
circumference
The circumference is the distance around the
circle.
Radius & Diameter
• The word radius (plural: radii) is also used to denote the length of a
radius (all radii have the same length).
• The word diameter is also used to denote the length of a diameter (all
diameters have the same length).
• Note that the diameter of a circle is twice its radius.
8
FORMULAS
• Diameter = 2 X Radius
• Radius = Diameter/2
• Circumference = 3.14 X Diameter
• Diameter = Circumference divided by 3.14
• Area = Radius X Radius X 3.14
Discussion:
Radius/Diameter
• Mom bought a coffee can with a
radius of 3 in. Will it fit on a shelf
that is 6 in. wide so that the
cupboard door will still close? Please
explain your answer using what we
have learn so far.
Discussions
Given information:
• Radius = 3 in
• Shelf = 6 in
Solve
Diameter = 2 x Radius
Diameter = 2 x 3
Diameter = 6 inches
Yes, the coffee can will fit the self because it has a diameter of 6 in.
Chords
• A chord is any line segment that joins two points on circle.
• Therefore, a diameter is an example of a chord. It is the longest possible
chord.
Question:
How many chords can a
Circle contain?
Explain your answer.
12
Parts of a Circle
radius
chord
diameter
R
K
Segments
of
Circles
A
J
G
K
K
T
Question: From the figures, you can tell that the diameter is a special type of _____ that
passes through the center.
ANSWER:
CHORD
Chords and Radii
• Given a chord in a circle, any radius that
bisects the chord (passes through its
midpoint) is perpendicular to that chord.
• Also, if a radius is perpendicular to a chord,
then it bisects the chord.
15
Distance to Chords
• The distance from the center of a circle to a
chord is measured along the radius that is
perpendicular to the chord.
• Chords that are the same distance from the
center are the same length.
• Also, chords that are the same length are the
same distance from the center.
16
Example
• In a circle of radius 5, a chord has length 8.
Find the distance to the chord (MC) from the
center of the circle.
Answer:
M
4
• Let C be the center of the circle and A and B
the endpoints of the chord. Let M be the
A
5
midpoint of the chord so that
• Then
• So, by the Pythagorean Theorem,
B
C
17
Video
Click this link to view the video: https://www.youtube.com/watch?v=Yb1HYyBfLfc
Ticket-Out-The-Door
Answer the following independently:
1. Identify/Name 3 parts of a circle. Draw and Label each part for full
credit.
1. What is the formula of diameter?
1. According to the video, what type of tools did they use to draw a
circular shape?