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10-3 Arc and Chords
You used the relationships between arcs and angles to find measures.
• Recognize and use relationships between arcs and chords.
• Recognize and use relationships between arcs, chords, and diameters.
Definition
A chord is a line segment with endpoints on a circle.
AB is a chord of ּסD
Where would you find the largest chord in any circle?
If the chord is not a diameter, then its endpoints divide the circle into a major and minor arc.
A
B
D
p. 715
Jewelry A circular piece of jade is hung from a
chain by two wires around the stone.
JM KL and = 90. Find .
A. 42.5
B. 85
C. 127.5
D. 170
A. 6
B. 8
C. 9
D. 13
If a line, segment, or ray divides an arc into two congruent arcs, then it bisects the arc.
p. 716
Answer:
A. 14
B. 80
C. 160
D. 180
Find the distance from chord PQ to the center of ּסO
• The radius of circle O is 13 mm. Draw a radius connecting it to one end of the chord.
• Draw the perpendicular bisector from the center to the chord.
• How long is PR?• What theorem do you use to
find the distance from the chord to the center of the circle?
• OR2 + 52 = 132
• OR = 12 mm
O
P Q10 mm
13 mm
R
CERAMIC TILE In the ceramic stepping
stone below, diameter AB is 18 inches long
and chord EF is 8 inches long. Find CD.
Step 1 Draw radius CE.
This forms right ΔCDE.
Step 2 Find CE and DE.
Since AB = 18 inches, CB = 9 inches. All
radii of a circle are congruent, so
CE = 9 inches.
Since diameter AB is perpendicular to EF,
AB bisects chord EF by Theorem 10.3. So,
DE = (8) or 4 inches.__12
A. 3.87
B. 4.25
C. 4.90
D. 5.32
In the circle below, diameter QS is 14 inches long and chord RT is 10 inches long. Find VU.
57
p. 717
Another way to determine if two chords in a circle are congruent is if they are the same distance from the center.
Since chords EF and GH are congruent, they
are equidistant from P. So, PQ = PR.
PQ = PR
4x – 3 = 2x + 3 Substitution
x = 3 Simplify.
So, PQ = 4(3) – 3 or 9
Answer: PQ = 9
A. 7
B. 10
C. 13
D. 15
10-3 Assignment
Page 718, 7-12, 16-17, 22-23
