10-6 Circles and Arcs


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10-6 Circles and Arcs

  1. 1. Essential Understanding You can find the length of part of a circle’s circumferences by relating it to an angle in the circle Students will be able to find the measures of central angles and arcs Students will be able to find the circumference and arc length
  2. 2. Vocabulary Circle: set of all points equidistant from a given point called the center  Named by its center. Ex. Circle P (P) Diameter: segment that contains the center and ahs both endpoints on the circle Radius: segment that has one endpoint at the center and the other endpoint on the circle Congruent circles: have congruent radii Central Angle: an angle whose vertex is the center of the circle
  3. 3. Parts of a Circle
  4. 4. Arcs Semicircle: type of arc called that is half of a circle  Named by its endpoints and another point on the arc Minor Arc: smaller than a semicircle  Named by its endpoints Major Arc: larger than a semicircle  Named by its endpoints and another point on the arc
  5. 5. Naming Arcs What are the minor arcs of A? What are the semicircle of A? What are the major arcs of A that contain point Q?
  6. 6. Arc Addition Postulate The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs. Arc ABC = arc AB + arc BC
  7. 7. Finding the Measures of Arcs
  8. 8. Circumference of a Circle Distance around the circle C = πd or C = 2πr All circles are similar to each other, therefore a similarity transformation can be done that maps any circle to another circle Concentric circles: coplanar circles that have the same center
  9. 9. Finding a Distance A car has a circular turning radius of 16.1 ft. The distance between the two front tires is 4.7 ft. How much farther does a tire on the outside of the turn travel than a tire on the inside?
  10. 10. Finding a Distance A merry-go-around has seats 7 feet from the center of the ride and 10 feet from the center. How much further does a child seated on the outside loop travel than a child seated on the inside loop in one complete revolution?
  11. 11. Arc Length Distance of a fraction of the circumference The length of an arc of a circle is the product of the ratio (measure of the arc) and the circumference of the circle. 360
  12. 12. Finding Arc Length in Red
  13. 13. Finding Arch Length What is the length of a semicircle with radius 1.3m? Leave your answer in terms of π.
  14. 14. Homework Pg. 654 #9 – 11, 12 – 27 (3s), 28 – 32, 43 15 problems