# 10.2 Arch and Chords

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```					                Bell work
Find the value of radius, x, if the diameter
of a circle is 25 ft.

25 ft

x
Unit 3 : Circles:
10.2 Arcs and Chords

Objectives: Students will:

1. Use properties of arcs and chords to
solve problems related to circles.
Words for Circles
1.    Central Angle
2.    Minor Arc
3.    Major Arc
4.    Semicircle
5.    Congruent Arcs
6.    Chord
7.    Congruent Chords
Are there any words/terms that you are
unsure of?
Label Circle Parts

1.   Semicircles   5. Exterior   9. Tangent
2.   Center        6. Interior   10. Secant
3.   Diameter      7. Diameter   11. Minor Arc
4.   Radius        8. Chord      12. Major Arc
Arcs of Circles
CENTRAL ANGLE – An angle with its
vertex at the center of the circle
Central Angle

A
CENTER P                   •
P
•    60º

•   B
Arcs of Circles
Minor Arc AB and Major Arc ACB
Central Angle

A
CENTER P                           •       MINOR ARC
P
AB
•    60º

MAJOR ARC              •                   •
C                           B
ACB
Arcs of Circles
The measure of the Minor Arc AB = the measure of the Central
Angle
The measure of the Major Arc ACB = 360º - the measure of the
Central Angle             Central Angle

A
CENTER P                      •       Measure of the
MINOR ARC =
P                  the measure of the
•    60º           Central Angle
The measure of the
MAJOR ARC =                  300º
360 – the measure of C   •                •        AB = 60º
B
the MINOR ARC

ACB = 360º - 60º
= 300º
Arcs of Circles
Semicircle – an arc whose endpoints
are also the endpoints of the diameter
of the circle; Semicircle = 180º

180º

•

Semicircle

The measure of an arc formed by two
adjacent arcs is the sum of the
measures of the two arcs
A
•                  •   C

AB + BC = ABC
170º
•   80º
170º + 8 0º = 2 5 0º

ARC ABC = 250º
•B
Example 1

X
•          •
Y

75º

P• 110°

•
Z

arcXY  75
arcYZ  110
arcXYZ  185
arcXZ  175
(p. 605)     Theorem 10.4
In the same circle or in congruent circles
two minor arcs are congruent iff their
corresponding chords are congruent
Congruent Arcs and Chords
Theorem
Example 1: Given that Chords DE is
congruent to Chord FG. Find the value
of x.         Arc DE = 100º

D                        E

F                   G

Arc FG = (3x +4)º
Congruent Arcs and Chords
Theorem

Arc DE = 100º

D                       E

F                   G

Arc FG = (3x +4)º
Congruent Arcs and Chords
Theorem
Example 2: Given that Arc DE is
congruent to Arc FG. Find the value
of x.
D                      E
Chord DE = 25 in

Chord FG = (3x + 4) in
F                   G
Congruent Arcs and Chords
Theorem

D                      E
Chord DE = 25 in

Chord FG = (3x + 4) in
F                   G
(p. 605)        Theorem 10.5

If a diameter of a circle is perpendicular to a chord,
then the diameter bisects the chords and its arcs.

Chord

Diameter

Congruent Arcs            P
•

Congruent
Segments
(p. 605)       Theorem 10.6

If one chord is the perpendicular bisector of another
chord then the first chord is the diameter

Chord 2
Chord 1: _|_ bisector
of Chord 2, Chord 1 =
the diameter

P
•
Diameter
(p. 606)       Theorem 10.7
In the same circle or in congruent circles, two
chords are congruent iff they are equidistant from
the center. (Equidistant means same perpendicular
distance)

Q
T
V
Chord TS  Chord QR
__   __                    •        R
iff PU  VU            U       P

S                Center P
Example
Find the value of Chord QR, if TS = 20
inches and PV = PU = 8 inches

Q
T
V
8 in

•       R
U            P
8 in

S                      Center P
Chord QR = 20 inches
(Theroem 10.7)
Home work
PWS 10.2 A

P. 607- 608 (12-46) even
Journal
Write two things about Arcs and
Chords related to circles from this
lesson.

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