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10.6 circles and arcs

The document defines key terms related to circles such as central angle, arc, semicircle, minor arc, and major arc. It provides examples of identifying these elements in circles and finding the measures of central angles and arcs. The document concludes with homework problems involving calculating measures of central angles and arcs in various circle graphs and diagrams.

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and Objective: Find the measures of central angles and arcs.
A CIRCLE is the set of all points equidistant from a given point called the center. This is circle P for Pacman. Circle P P
A CENTRAL ANGLE of a circle is an angle with its vertex at the center of the circle. Central angle
An arc is a part of a circle. In this case it is the part Pacman would eat.  Arc
One type of arc, a semicircle, is half of a circle. P A C Semicircle ABC m ABC = 180 B
A minor arc is smaller than a semicircle.
A major arc is greater than a semicircle.
A minor arc is smaller than a semicircle. A major arc is greater than a semicircle.
R S P RS is a minor arc. mRS = m RPS.
L N M O LMN is a major arc. mLMN = 360 – mLN
R S P L N M RS is a minor arc. mRS = m RPS. O LMN is a major arc. mLMN = 360 – mLN
A C D Identify the following in circle O: 1) the minor arcs EO
A C D Identify the following in circle O: 1) the minor arcs EO AD
A C D Identify the following in circle O: 1) the minor arcs EO AD, CE
A C D Identify the following in circle O: 1) the minor arcs EO AD, CE, AC,
A C D Identify the following in circle O: 1) the minor arcs EO AD, CE, AC, & DE
A C D Identify the following in circle O: 1) the minor arcs EO AD, CE, AC, & DE
A C D Identify the following in circle O: 2) the semicircles EO
A C D Identify the following in circle O: 2) the semicircles EO ACE
A C D Identify the following in circle O: 2) the semicircles EO ACE, CED
A C D Identify the following in circle O: 2) the semicircles EO ACE, CED, EDA
A C D Identify the following in circle O: 2) the semicircles EO ACE, CED, EDA, & DAC
A C D Identify the following in circle O: 2) the semicircles EO ACE, CED, EDA, & DAC
A C D Identify the following in circle O: 3) the major arcs containing point A EO
A C D Identify the following in circle O: 3) the major arcs containing point A EO ACD
A C D Identify the following in circle O: 3) the major arcs containing point A EO ACD, CEA
A C D Identify the following in circle O: 3) the major arcs containing point A EO ACD, CEA, EDC
A C D Identify the following in circle O: 3) the major arcs containing point A EO ACD, CEA, EDC,& DAE
A C D Identify the following in circle O: 3) the major arcs containing point A EO ACD, CEA, EDC,& DAE
The measure of a central angle is equal to its intercepted arc. 53o 53o O P R
The measure of a central angle is equal to its intercepted arc. 53o 53o O P R
Find the measure of each arc. 1. BC = 2. BD = 3. ABC = 4. AB =
Find the measure of each arc. 1. BC = 32 2. BD = 3. ABC = 4. AB =
Find the measure of each arc. 1. BC = 32 2. BD = 3. ABC = 4. AB =
Find the measure of each arc. 1. BC = 32 2. BD = 90 3. ABC = 4. AB =
Find the measure of each arc. 1. BC = 32 2. BD = 90 3. ABC = 180 4. AB =
Find the measure of each arc. 1. BC = 32 2. BD = 90 3. ABC = 180 4. AB = 148
Here is a circle graph that shows how people really spend their time. Find the measure of each central angle in degrees. 1. Sleep 2. Food 3. Work 4. Must Do 5. Entertainment 6. Other
Here is a circle graph that shows how people really spend their time. Find the measure of each central angle in degrees. 1. Sleep 2. Food 3. Work 4. Must Do 5. Entertainment 6. Other
Here is a circle graph that shows how people really spend their time. Find the measure of each central angle in degrees. 1. Sleep 2. Food 3. Work 4. Must Do 5. Entertainment 6. Other
Here is a circle graph that shows how people really spend their time. Find the measure of each central angle in degrees. 1. Sleep 2. Food 3. Work 4. Must Do 5. Entertainment 6. Other
Here is a circle graph that shows how people really spend their time. Find the measure of each central angle in degrees. 1. Sleep 2. Food 3. Work 4. Must Do 5. Entertainment 6. Other
Here is a circle graph that shows how people really spend their time. Find the measure of each central angle in degrees. 1. Sleep 2. Food 3. Work 4. Must Do 5. Entertainment 6. Other
Here is a circle graph that shows how people really spend their time. Find the measure of each central angle in degrees. 1. Sleep 2. Food 3. Work 4. Must Do 5. Entertainment 6. Other
Here is a circle graph that shows how people really spend their time. Find the measure of each central angle in degrees. 1. Sleep 2. Food 3. Work 4. Must Do 5. Entertainment 6. Other
Here is a circle graph that shows how people really spend their time. Find the measure of each central angle in degrees. 1. Sleep 2. Food 3. Work 4. Must Do 5. Entertainment 6. Other
Here is a circle graph that shows how people really spend their time. Find the measure of each central angle in degrees. 1. Sleep 2. Food 3. Work 4. Must Do 5. Entertainment 6. Other
Homework: page 569 (1 – 26)