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1. 3x=x+502. y+5y+66=3603. x+14x=1804. a2+16=25
Solve the equations
Note: A diameter is a chord but not all chords are diameters
10.2 ARCS AND CHORDS
Measure of minor arc = measure of central angle
Measure of major arc = 360 – central angle
B
central angle
minor arcs
AC
CB€
Major arcs
ABC
CAB
Semicircle
ACB
centerdiameter
chord
radius
A
C
O
The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.
mABC = mAB + mBC
Postulate 26- Arc Addition Postulate
If the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
Theorem 10.4
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AB ≅ BC iff AB ≅ BC.
Are the arcs congruent?1. 2.
yes
No
Arcs AB and CD Arcs XY and ZW
If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
Theorem 10.5
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DE ≅ EF, DG ≅ GF
If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.
Theorem 10.6
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JK is a diameter of the circle.
In the same circle, or in congruent circles, two chords are congruent iff they are equidistant from the center.
Theorem 10.7
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AB ≅CD iff EF ≅ EG.
Find the measure of each arc of ⨀A.
a) BD
b) BE
c) BED
Practice Time!
1250
1370
2350
Find mBC.
1220
How to locate the center of the following circle using the chords shown.
AB=12, DE = 12, and CE= 7. Find CG.
€
13
The graph shows the percent of each type of bicycle sold in the U.S. in 2001
Find the measurement of the central angle representing each category. List them from least to greatest.
25.20,32.40, 75.60, 93.60, 133,20
≈14.66 cm
What is the arc measure when the minute hand on a clock move in 10 minutes? How far will the tip of a 14cm long minute hand travel?
€
πd10
60
Which is closer to the center of a circle? A longer chord or a shorter chord? Explain.
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