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Solve the equations. 3x=x+50 y+5y+66=360 x+14x=180 a 2 +16=25. 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. minor arc. chord.

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Solve the equations
Solve the equations

  • 3x=x+50

  • y+5y+66=360

  • x+14x=180

  • a2+16=25

Note: A diameter is a chord but not all chords are diameters



  • 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

minor arc

chord

major arc


Two ways to measure arcs
Two Ways To Measure Arcs:

  • central angle: in degrees

  • the length of the arc: in radians


Measure of minor arc measure of central angle measure of major arc 360 central angle
Measure of minor arc = measure of central angleMeasure of major arc = 360 – central angle

C

radius

minor arcs

AC

CB

central angle

Major arcs

ABC

CAB

chord

A

B

center

diameter

O

Semicircle

ACB


Postulate 26 arc addition postulate
Postulate 26- Arc Addition Postulate

  • The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

    mABC = mAB + mBC


Theorem 10 4
Theorem 10.4

  • If the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.


Are the arcs congruent
Are the arcs congruent?

1.

Arcs AB and CD

2.

Arcs XY and ZW

yes

No


Theorem 10 5
Theorem 10.5

  • If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.


Theorem 10 6
Theorem 10.6

  • If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.


Theorem 10 7
Theorem 10.7

  • In the same circle, or in congruent circles, two chords are congruent iff they are equidistant from the center.


Practice time
Practice Time!

  • Find the measure of each arc of ⨀A.

  • BD

  • BE

  • BED

1250

1370

2350


Find mbc
Find mBC.

How to locate the center of the following circle using the chords shown.

1220



The graph shows the percent of each type of bicycle sold in the u s in 2001
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


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?

  • ≈14.66 cm



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