1 / 18

7-6 Circles and Arcs M11.C.1

7-6 Circles and Arcs M11.C.1. Objectives: To find the measures of central angles and arcs To find circumference and arc length. Vocabulary. In a plane, a circle is the set of all points equidistant from a given point called the center . You name a circle by its center. Circle P (OP).

zanna
Download Presentation

7-6 Circles and Arcs M11.C.1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 7-6 Circles and Arcs M11.C.1 Objectives: To find the measures of central angles and arcs To find circumference and arc length

  2. Vocabulary In a plane, a circle is the set of all points equidistant from a given point called the center. You name a circle by its center. Circle P (OP). 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 diameter is a segment that contains the center of a circle and has both endpoints on the circle. A central angle is an angle whose vertex is the center of the circle. Circle P

  3. Example: Real World A researcher surveyed 2000 members of a club to find their ages. The graph shows the survey results. Find the measure of each central angle in the circle graph.

  4. Vocabulary An arc is a part of a circle. One type of arc, a semicircle, is half of a circle. A minor arc is smaller than a semicircle. A major arc is greater than a semicircle.

  5. Naming an Arc • Semicircle Minor Arc Major Arc -3 letters -2 letters -3 letters • Equals 180 -Equals the -Equals 360 measure of the minus the central angle minor arc

  6. Example: Identifying Arcs Identify the minor arcs, major arcs, and semicircles in circle P with point A as an endpoint.

  7. Vocabulary Adjacent Arcs – are arcs of the same circle that have exactly one point in common.

  8. Postulate 7-1: Arc addition postulate The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

  9. Example: Finding the measures of arcs Find the m XY and m DXM in circle C

  10. Vocabulary The circumference of a circle is the distance around the circle. The number pi (π) is the ratio of the circumference of a circle to its diameter.

  11. Circumference of a Circle The circumference of a circle is π times the diameter. C = πd or C =2πr

  12. Vocabulary Circles that lie in the same plane and have the same center are concentric circles.

  13. Example: Real World A circular swimming pool with a 16 foot diameter will be enclosed in a circular fence 4 feet from the pool. What length of fencing material is needed? Round to the nearest whole number.

  14. Vocabulary The measure of an arc is in degrees while the arc length is a fraction of a circle’s circumference.

  15. Arc Length The length of an arc of a circle is the product of the ratio measure of the arc and the circumference 360 of the circle.

  16. Finding Arc Length Find the length of ADB in circle M in terms of π.

  17. Vocabulary Congruent Arcs – are arcs that have the same measure and are in the same circle or in congruent circles.

  18. Homework Handed-In Page 390 #27-32, 34-39, 41-47, 52, 53, 63-65

More Related