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

An arc is a portion of the circumference of a circle.

A chord is a line segment drawn between the end points of the arc

chord

major arc

minor arc

central angle: in degrees

Two Ways To Measure Arcs:

the length of the arc: in radians

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.

yesNo

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.

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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?

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πd1060

Which is closer to the center of a circle? A longer chord or a shorter chord? Explain.