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Understanding Central Angles and Arcs in Circles

This lesson focuses on finding the measures of central angles and arcs within circles. A circle is defined as a set of points equidistant from a center point, exemplified by Circle P for Pacman. A central angle has its vertex at the circle's center, whereas an arc represents a portion of the circle, such as the area Pacman would consume. We explore semicircles, minor arcs, and major arcs, with examples to practice measuring each type. The lesson includes homework to solidify understanding of circular measurements.

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Understanding Central Angles and Arcs in Circles

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  1. 10.6 Circles and Arcs Objective: Find the measures of central angles and arcs.

  2. A CIRCLEis the set of all points equidistant from a given point called the center. This is circle P for Pacman. Circle P P

  3. Central angle A CENTRAL ANGLEof a circle is an angle with its vertex at the center of the circle.

  4. Arc An arc is a part of a circle. In this case it is the part Pacman would eat. 

  5. Semicircle ABC m ABC = 180 One type of arc, a semicircle, is half of a circle. C P B A

  6. A minor arc is smaller than a semicircle. A major arc is greater than a semicircle. less than 180 more than 180

  7. LMN is a major arc. mLMN = 360 – mLN RS is a minor arc. mRS = m RPS. S P R N O M L

  8. Identify the following in circle O: 1) the minor arcs C A O E D

  9. Identify the following in circle O: 2) the semicircles C A O E D

  10. Identify the following in circle O: 3) the major arcs containing point A C A O E D

  11. R 53o 53o P O The measure of a central angle is equal to its intercepted arc.

  12. Find the measure of each arc. • BC = 32 • BD = 90 • ABC = 180 • AB = 148

  13. Here is a circle graph that shows how people really spend their time. Find the measure of each central angle in degrees. • Sleep • Food • Work • Must Do • Entertainment • Other

  14. THE END Homework: page 569 (1 – 26)

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