Lauretta J. Fox
Not all geometric figures are formed by straight lines. One of the most useful geometric shapes is the circle. It plays a vital part in our lives—in wheels, in all sorts of containers, in machine parts, in design, and in architecture. The circle provides the most economical form of shelter. Round houses are used in the Arctic and at the equator.
A
circle
is the set of points in a plane equidistant from a fixed point in the plane called the center. The circle receives its name from the center. O is the symbol used to denote a circle.
Several important terms are associated with the circle. A
radius
of a circle is a line segment which Joins the center to any point on the circle. AB is a radius of circle A.
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A
chord
is a line segment whose endpoints lie on the circle. CD is a chord of circle A. A
diameter
is a chord which passes through the center of the circle. CE is a diameter of circle A. A
secant
is a line which intersects a circle in two points. FG is a secant of circle A.
A
tangent
is a line which lies in the plane of the circle and intersects the circle in exactly one point. EJ is a tangent to circle A. The
point of contact
is the point at which the tangent intersects the circle. ~ is the point of contact of tangent EJ. The
circumference
of a circle is the perimeter or distance around the edge of the circle. An
arc
is a part of the circumference of a circle. EB is an arc of circle A.
If the circumference of any circle is divided by its diameter, the quotient is always approximately 22/7 or 3.14. This special number is represented by the Greek letter pi (). Hence, the circumference of a circle may be expressed as the product of pi and the length of the diameter of the circle. The formula for finding circumference is C = d or C = 2 r. The area of a circle may be expressed as the product of pi and the square of the length of the radius, or A = r2 .
Example:
Find the circumference and area of a circle whose diameter is 14 inches long.
Solution:
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C = d
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A = r2
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C = 22/7 x 14
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A = 22/7 x 7 x 7
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C = 44 inches
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A = 154 sq. in..
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Suggested Assignment:
Write a report on circular houses used in Africa and in the Arctic.
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Exercises:
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1. Find the circumference and area of a circle whose radius is 5 1/4 feet long.
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2. In circle X, identify the following parts:
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a. RY
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e. Line ST
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b. XZ
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f. Line UV
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c. YW
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g. Point R
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d. ZW
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h. Point X
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(figure available in print form)
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3. Illustrated below are floor plans of a round house, a square house, and a rectangular house. The perimeter of each one is 66 feet. Find the area of each figure Which of the houses has the greatest number of square feet of living area?
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(figure available in print form)
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4. Name the geometric figures that you see in the illustration of the door below at the left.
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5. How many square inches of glass are necessary to fill the window shown below at the right?
(figure available in print form)
