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# Solve the equations - PowerPoint PPT Presentation

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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• 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

### 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

major arc

• central angle: in degrees

• the length of the arc: in radians

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

C

minor arcs

AC

CB

central angle

Major arcs

ABC

CAB

chord

A

B

center

diameter

O

Semicircle

ACB

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

mABC = mAB + mBC

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

1.

Arcs AB and CD

2.

Arcs XY and ZW

yes

No

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

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

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

• Find the measure of each arc of ⨀A.

• BD

• BE

• BED

1250

1370

2350

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

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