10-3 Arc and Chords You used the relationships between arcs and angles to find measures. Recognize...
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![Page 1: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062314/56649eb65503460f94bbf5a3/html5/thumbnails/1.jpg)
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.
![Page 2: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062314/56649eb65503460f94bbf5a3/html5/thumbnails/2.jpg)
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
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p. 715
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Jewelry A circular piece of jade is hung from a
chain by two wires around the stone.
JM KL and = 90. Find .
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A. 42.5
B. 85
C. 127.5
D. 170
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A. 6
B. 8
C. 9
D. 13
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If a line, segment, or ray divides an arc into two congruent arcs, then it bisects the arc.
p. 716
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Answer:
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A. 14
B. 80
C. 160
D. 180
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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
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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
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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
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p. 717
Another way to determine if two chords in a circle are congruent is if they are the same distance from the center.
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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
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A. 7
B. 10
C. 13
D. 15
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10-3 Assignment
Page 718, 7-12, 16-17, 22-23