
Geometry and
the Circle 

Unit 2
> Lesson 1 of 6 
A circle is an important shape in the field of geometry. Let's look at the definition of a circle and its parts.
We will also examine the relationship between the circle and the plane. 
A circle is a shape with all points the same distance from its center. A circle is named by
its center. Thus, the circle to the right is called circle A since its center is at
point A.
Some real world examples of a circle are a wheel, a dinner plate and (the
surface of) a coin.




The distance across a circle through the center is called the diameter.
A realworld example of diameter is a 9inch plate. 



The radius of a circle is the distance from the center of a circle
to any point on the circle. If you place two
radii
endtoend in a circle, you would have the same length as one diameter. Thus, the diameter of a circle is twice as long as the radius.




We can look at a pizza pie to find realworld examples of diameter and radius.
Look at the pizza
to the right which has been sliced into 8 equal parts through its
center. A radius is formed by making a straight cut from the center to a point on the circle.
A straight cut made from a point on the circle, continuing through its center to
another point on the circle, is a diameter. As you can see, a
circle has many different radii and diameters, each passing through
its center.




A chord is a
line segment
that joins two points on a curve. In
geometry, a chord is often used to describe a line segment joining two
endpoints that lie on a circle. The circle to the right contains chord AB. If
this circle was a pizza pie, you could cut off a piece of pizza along
chord AB. By cutting along chord AB, you are cutting off a segment of pizza that
includes this chord. 



A circle has many different chords. Some chords pass through the center
and some do not. A chord that passes through the center is called a
diameter.




It turns
out that a diameter of a circle is the longest chord of that circle since it
passes through the center. A diameter satisfies the definition
of a chord, however, a chord is not necessarily a diameter. This is
because every diameter passes through the center of a circle, but some
chords do not pass through the center. Thus, it can be stated, every
diameter is a chord, but not every chord is a diameter.




Let's revisit the definition of a circle. A circle is the set of points that are
equidistant from a special point in the plane. The special point is the center.
In the circle to the right, the center is point A. Thus we have circle A.




A plane is a
flat surface that extends without end in all directions. In the diagram to the
right, Plane P contains points A, B and C. 


Can you think of some
real world objects that satisfy the definition of a plane? At this level of mathematics,
that is difficult to do. Intuitively, a plane may be visualized as a flat infinite sheet of
paper. The top of your desk and a chalkboard are objects which can be used to represent a plane,
although they do not satisfy the definition above.



A circle divides the plane into three parts:
 the points INSIDE the circle
 the points OUTSIDE the circle
 and the points ON the circle




the points inside the circle 
the points outside the circle 
the points on the circle 
Example 1: 
Name the center of this circle.


Answer: 
Point B 

Example 2: 
Name two chords on this circle that are not diameters.


Answer: 
DE and FG 

Example 3: 
Name all radii on this circle.


Answer: 
BA, BC,
BD and BG 

Example 4: 
What are AC
and DG?


Answer: 
AC and DG
are diameters. 

Example 5: 
If DG is 5
inches long, then how long is DB?


Solution: 
The diameter of a circle is twice as long as the radius. 

5 inches ÷ 2 = 2.5 inches 
Answer: 
The length of DB
is 2.5 inches 
Summary: 
A circle is a shape with all points the same distance from its center. A circle is named by
its center. The parts of a circle include a radius, diameter and a chord. All
diameters are chords, but not all chords are diameters.
A plane is a
flat surface that extends without end in all directions. A circle divides the plane into three parts:
The points inside the circle, the points outside the circle and the points
on the circle.

Exercises
Directions: Refer to the diagram to answer each question below. Select your answer by clicking on its button. Feedback to your answer
is provided in the RESULTS BOX. If you make a mistake, choose a different button. 
1. Which of the following is a chord, but not
a diameter?





2. Which of the following is a radius?





3. Name the center of this
circle.





4. What is PR
(or PQR)?





5. If PQ
is 3 cm long, then how long is PR?




This lesson is by Gisele Glosser. You can find me on Google.
