Download Section 10.3 ~ Chords and Arcs!!

Geometry
Name ______________________
Date ____________ Hour ______
Section 10.3 ~ Chords and Arcs!!
L.T.: Be able to use congruent chords, arcs, and central
angles to find unknowns!
Quick Review:
Name two minor arcs on the circle.
A
AB, BC
B
Name one major arc. ABD
What is the relationship between the measure of
an arc and the measure of its central angle?
D
=
C
Theorem:
Within a circle or within two congruent circles:
congruent central angles have congruent chords
congruent chords have congruent arcs
congruent arcs have congruent central angles
Ex. 1: The two circles are congruent. Given that
minor arcs BC and DF are also congruent, what else
can you conclude?
D
B
∠BOC = ∠DPF
Quick Vocab:
Chord:
BC = DF
segment whose endpoints
are on a circle
F
O
C
Theorem:
Theorems:
Within a circle or within two congruent circles:
In a circle, a diameter that is perpendicular to a
chord bisects the chord and its arcs.
chords equidistant from the center are
congruent (distance must be perpendicular)
congruent chords are equidistant from the center
In a circle, a diameter that bisects a chord is
perpendicular to the chord.
Ex. 2: Find the value of each variable.
12.5
9 x
9
12.5
x = 12.5
P
18
18
16
In a circle, the perpendicular bisector of a chord
passes through the center of the circle.
x
36
x = 16
NOTE: In these theorems, “diameter” refers to any
segment that passes through the center of the circle.
1
Geometry
Name ______________________
Date ____________ Hour ______
Practice is GOOD! ☺
Ex. 3: Find each missing length to the nearest tenth.
15
11
x
7
14 cm
6.8
x
3 cm
y
11
x2 = 32 + 72
x2 + 112 = 152
x2 = 9 + 49
x2 = 58
x2 + 121 = 225
x2 = 104
x = 7.6 cm
4
x
y2 + 42 = 6.82
y2 + 16 = 46.24
y2 = 30.24
y = 5.5
x = 10.2
Ex. 4: In the third circle above, find the
distance from the midpoint of the chord
to the midpoint of its minor arc.
x = 11
Can you use congruent
chords, arcs, and central
angles to find unknowns?
Start the homework!! ☺
6.8 – 4
2.8
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