Botten Adv Geom Notes
Section 10­1 Circles and Circumference
­ A circle is the locus of all points in a plane
equidistant from a given point called the center of
the circle.
­ A circle is usually named by its center point.
­ The figure below shows circle C, which can be
written as C.
­ Several special segments in circle C are also
shown.
­ Note that diameter BE is made up of collinear
radii CB and CE.
­ The plural of radius is radii.
­ Note also that a diameter is also a chord, but a
chord is not a diameter unless it goes through
the center of the circle.
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­ By definition of a circle, the distance from the
center to any point on the circle is always the
same.
­ Therefore, all radii are congruent.
­ A diameter is composed of two radii, so all
diameters are congruent.
­ The letters d and r are usually used to represent
diameter and radius in formulas.
­ So, which means ­ And, which means Ex 1 Refer to the circle below to answer the following questions.
a. Name the circle.
b. Name all of the radii of the circle.
c. Name all of the chords of the circle.
d. Name a radius not drawn as part of a diameter.
e. Name a diameter of the circle.
f. Is ? Explain.
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Ex 2 Circle A has diameters DF and PG.
a. If DF = 10, find DA.
b. If PA = 7, find PG.
c. If AG = 12, find LA.
Ex 3 The diameters of circle L and circle M are 20 and 13 units, respectively. Find each measure if QR = 4.
a. LQ
b. RM
­ The circles shown in the example above have
different radii.
­ They are not congruent circles.
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­ For two circles to be congruent circles, they must
have congruent radii or congruent diameters.
­ The circumference of a circle is the distance
around the circle.
­ Circumference is most often represented by the
letter C.
­ There are 2 formulas that you can use to find the
circumference of a circle.
­ The formula that you use depends upon whether
you are given the radius or the diameter of the
circle.
­ So, if you know the diameter or radius, you can
find the circumference.
­ Likewise, if you know the circumference, you
can find the diameter or radius.
­ We will use the key on our calculators in
these formulas.
Ex 4 Find the circumference of a circle with the given radius or diameter. Round to the nearest hundredth.
a. r = 8 cm
b. c. d = 10 in
d. 4
Ex 5 The radius, diameter, or circumference of a circle is given. Find the missing measures to the nearest hundredth.
a. r = 8 cm
d = ___________ , C = _____________
b. d = 9 m
r = ___________ , C = _____________
c. C = 35.7 in
d = ___________ , r = ______________
­ You can also use other geometric figures to help
you find the circumference of a circle.
­ If the directions ever say to find the exact
circumference, then you would leave your answer
as something like 10 , instead of multiplying it
out.
Ex 6 Find the exact circumference of each circle.
a.
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b.
c.
Assign Pgs. 525 ­ 528 # 16 ­ 55, 65, 75 ­ 80
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