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10.6 Circles and Arcs

10.6 Circles and Arcs. In a plane, a circle is the set of all points equidistant from a given point called the center . A diameter is a segment that contains the center of a circle and has both endpoints on the circle.

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10.6 Circles and Arcs

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  1. 10.6 Circles and Arcs • In a plane, a circle is the set of all points equidistant from a given point called the center. • A diameter is a segment that contains the center of a circle and has both endpoints on the circle. • A radius is a segment that has one endpoint at the center and the other endpoint on the circle. • Congruent circles have congruent radii. • A central angle is an angle whose vertex is the center of the circle. • Way to write the name of a circle:

  2. Circles • An arc is a part of a circle. • A semicircle is one type of arc – half of a circle. • A minor arc is smaller than a semicircle. • A major arc is larger than a semicircle. • You name a minor arc by its endpoints and a major arc or a semicircle by its endpoints and another point on the arc.

  3. Naming Arcs • What are the minor arcs of circle O? • What are the semicircles of circle O? • What are the major arcs of circle O that contain point A?

  4. Arc Measure • The measure of a minor arc is equal to the measure of its corresponding central angle. • The measure of a major arc is the measure of the related minor arc subtracted from 360. • The measure of a semicircle is 180.

  5. Adjacent Arcs • Adjacent arcs are arcs of the same circle that have exactly one point in common. • You can add the measures of adjacent arcs just as you can add the measures of adjacent angles.

  6. Arc Addition Postulate • The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

  7. Finding the Measures of Arcs • What is the measure of each arc in circle O? A. B. C. D.

  8. Circumference • The circumference of a circle is the distance around the circle. • The number pi ( ) is the ratio of the circumference of a circle to its diameter.

  9. Concentric Circles • Coplanar circles that have the same center are concentric circles.

  10. Arc Length • The measure of an arc is in degrees while the arc length is a fraction of a circle’s circumference.

  11. Finding Arc Length • What is the length of the arc shown in red? Leave your answer in terms of .

  12. Congruent Arcs • Congruent arcs are arcs that have the same measure and are in the same circle or in congruent circles.

  13. More Practice!!!!! • Homework – p. 654 # 9 – 23. • Homework – p. 654 – 655 # 24 – 35.

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