Essential UnderstandingEssential Understanding  You can find the length of part of a circle’s circumferences by relating it to an angle in the circle.

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Presentation transcript:

Essential UnderstandingEssential 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

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

Parts of a CircleParts of a Circle

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

Naming ArcsNaming 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?

Arc Addition PostulateArc 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

Finding the Measures of Arcs

Circumference of a CircleCircumference 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

Finding a DistanceFinding 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?

Finding a DistanceFinding 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?

Arc LengthArc 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

Finding Arc Length in RedFinding Arc Length in Red

Finding Arch LengthFinding Arch Length  What is the length of a semicircle with radius 1.3m? Leave your answer in terms of π.

Homework  Pg. 654  #9 – 11, 12 – 27 (3s), 28, 29, 30 – 32, 43  15 problems