Arcs and Chords
Section 10.3
Vocabulary
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Inscribed polygon – a polygon where all
vertices lie on the circle
B
Not inscribed B
C
C
G
H
A
F
A
D
E
F
D
E
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Circumscribed - a circle is
circumscribed about a polygon when it
contains all of the vertices of the
B
C
polygon
G
A
F
D
E
.
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Ex. 2
A circle is circumscribed about a regular
pentagon. What is the measure of the
arc between each pair of consecutive
vertices?
A. 60 B. 72 C. 36 D. 30
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Theorem 10.3
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Ex. 3 Circle O has a radius of 13 in.
Radius OB is perpendicular to chord,CD
which is 24 inches long.
A. If mCD  134 , find mBC
OB bisects CD
1
mBC  134   67
2
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B. Find OX
CXO is a right
triangle with
CO = 13
OB bisects CD so CX = 12
Use Pythagorean Theorem to find OX.
122 + OX2 = 132
OX = 5
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Circle R has a radius of 16 cm. Radius
RU is perpendicular to chord TV
which is 22 cm.
A. if mTV  110 , find mUV
B. Find RS
Ex 4
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Chords AC and DF are equidistant from the center. If the
radius of circle G is 26, find AC and DE.
Since AC and DF are equidistant from G then AC  DF
AG and GF are radii and form 2 right triangles. Use the
Pythagorean theorem to solve for AB.
AB2  102  262
AB = 24
AC = 48 so DF = 48 and DE = 24
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Chords MO and PR are equidistant from
the center. If the radius of circle S is
15, find MO and PQ.
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The radius of a circle is 22 cm and a
chord is 40 cm. How far is the chord
from the center of the circle?
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A chord of a circle is 50 in. and 12 in
from the center of a circle. Find the
radius.