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I 5 2 GEOMETRY.
Circles.
F
1
5" 12
J/ The Circle is a plane figure bound-
ed by a curved line called the circum-
ference or perphery, which is at all
points the same distance from a fixed
point in the plane, and this point is
called the center of the circle. ( See
point c, Fig. 12).
A Dia?neter is a straight line
passing through the center of a circle or
a sphere, terminating at the circumfer-
Circle. ence or surface. (See line e-d, Fig. 12).
A Radius is a straight line from the cenler to the circum-
ference of circle or sphere. ( See line c-f, Fig. 12).
Diameter = 2 X radius. The ratio of the circumference to
the diameter of a circle is usually denoted by the Greek letter tt
and is expressed approximately by the number 3.1416 or
22 qi
~f T°
Thus, if the circumference is required, multiply the diameter
by 3.1416. If the diameter is required, divide the circumference
by 3.1416.
A Chord is a straight line terminating at the circumference
of a circle but not passing through the center of the circle. ( See
line a-b, Fig. 12). The curved line a-b, or any other part of the
circumference of a circle, is called an arc.
Any surface bounded by the chord and an arc, like the
shaded surface a-b, is called a segment.
Any surface bounded by an arc and its two radii, like the
shaded surface c-f-d, is called a sector.
PROPERTIES OF THE CIRCLE.
Circumference = Diameter X 3.1416
Area = (Diameter)2
X 0.7854
Diameter = Circumference X 0.31831
Diameter
0.7854
Diameter = 1.1283 X V area
Circumference = 3.5449 X */ area
Length of any arc == Number of degrees X 0.017453 X radius.
Length of arc of 1 Degree when radius is 1 is 0.017453.
Length of an arc of 1 Minute when radius is 1 is 0.000290888.
Length of an arc of 1 Second when radius is 1 is 0.000004848.
When the length of the arc is equal to the radius the angle
is 57° 17’ 45" = 57.2957795 degrees.
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