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10-6: Circles and Arcs

Goal: Be able to find the measures of central angles and arcs, and to find the circumference and arc length of circles. 10-6: Circles and Arcs. circle – the set of all points ______________ from a given point, the __________. . equidistant. center. This is . center. A. (circle A).

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10-6: Circles and Arcs

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  1. Goal: Be able to find the measures of central angles and arcs, and to find the circumference and arc length of circles. 10-6: Circles and Arcs circle – the set of all points ______________ from a given point, the __________. equidistant center This is center A (circle A)

  2. radius – a segment that has one __________ at the __________ and the other endpoint on the _________. endpoint center circle diameter – a segment that contains the __________ of a circle and has both __________on the circle. center endpoints C is a radius. are also radii. A is a diameter. B D

  3. central angle– an angle whose _________ is at the __________ of the circle. vertex center C is a central angle. A is a central angle. B D There are ________ degrees in a circle. 360

  4. The following information was determined from a survey determining how people really spend their time. 7% 31% 18% 20% 15% 9% Directions: Find the measure of each central angle to the nearest whole number. Find the corresponding percent of 360. 1.) Sleep 4.) Work 2.) Other 5.) Entertainment 3.) Food 6.) Must Do

  5. arc – part of a _________. circle is a minor arc. is a major arc. ***The measure of a minor arc __________ the measure of its corresponding ______________ equals is a semicircle. central angle.

  6. Identify the following in circle C. M Y C W D X a.) two minor arcs _____________________________ b.) two major arcs _____________________________ c.) two semicircles _____________________________

  7. Find the measure of each arc. M 84° Y C 40° W 84° 56° D 56° 84° X so, is a semicircle. So, so,

  8. circumference of a circle – the ___________ around the circle. distance or r d Circles that lie in the same plane and have the same center are ___________________. concentric circles

  9. A car has a turning radius of 16.1 feet. 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? To find the radius of the inner circle, subtract 4.7 ft from the turning radius. circumference of outer circle: radius of the inner circle: circumference of inner circle: The difference of the two distances: A tire on the turning circle travels about 29.5 ft farther than a tire on the inner circle.

  10. Arc Length – fraction of the_______________ of a circle. circumference length of r r No. Is ? but 105 105 They are part of different circles with different radii. Congruent arcs – arcs that have the _________________ and are __________________ or ___________________. same measure in the same circle in congruent circles.

  11. Find the length of the arcs.

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