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.
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| The distance across a circle through the center is called the diameter.
A real-world example of diameter is a 9-inch plate. |
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| 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
end-to-end 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.
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We can look at a pizza pie to find real-world 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.
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| 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. |
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| 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.
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| 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.
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| 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.
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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. |
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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.
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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?
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2. Which of the following is a radius?
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3. Name the center of this
circle.
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4. What is PR
(or PQR)?
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5. If PQ
is 3 cm long, then how long is PR?
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