Chapter 10: Area 10.6 Circles & Arcs. Definitions circle: set of all points equidistant from a given point center: point that is equidistant from the.

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Presentation transcript:

Chapter 10: Area 10.6 Circles & Arcs

Definitions circle: set of all points equidistant from a given point center: point that is equidistant from the circle radius: segment that has one endpoint at the center and the other endpoint on the circle congruent circles: have congruent radii

Definitions diameter: segment that contains the center of a circle and has both endpoints on the circle central angle: angle whose vertex is the center of the circle

Example 1 In the circle graph from a hour-by-hour survey of 3600 people, what is the measure in degrees of the entertainment part?

Definitions arc: a piece of a circle semicircle: half of a circle minor arc: smaller than a semicircle major arc: greater than a semicircle

Example 2 Identify the following: the minor arcs the semicircles the major arcs that contain point A

Adjacent Arcs arcs of the same circle that have exactly one point in common can add the measures of adjacent arcs like adjacent angles

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

Example 3 Find the measure of each arc: BC BD ABC AB

Circumference of a Circle The circumference of a circle is π times the diameter.

Concentric Circles circles that lie in the same plane and have the same center

Example 4 A car has a turning radius of 16.1 ft. The distance between the two front tires is 4.7 ft. In completing the (outer) turning circle, how much farther does a tire travel than a tire on the concentric inner circle?

Example 4a The diameter of a bicycle wheel is 22 in. To the nearest whole number, how many revolutions does the wheel make when the bicycle travels 100 ft?

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

Example 5 Find the length of the arc XY.

Example 5 Find the length of arc XY.

Homework P even, 18, 20, 22, 28, 30, 36, 53

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