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Mrs. Scott Modern Geometry Name:___________________________________ Date:____________________________________ 7.6 Circles and Arcs Learning Objectives 1. To find the measure of central angles and arcs. 2. To find circumference and arc length. In a plane, a _______________________ is the set of all points equidistant from a given point called the ________________. You name a circle by its center. Picture: A _________________________ is a segment that has one endpoint at the center and the other endpoint on the circle. Let’s draw radius PC in the circle above. ______________________________ __________ have congruent radii. A ________________________________ is a segment that contains the center of a circle and has both endpoints on the circle. Let’s draw diameter AB in the circle above. A ____________________ _______________ is an angle whose vertex is the center of the circle. Let’s draw central angle APC in the circle above. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ An ______________ is part of a circle. One type of arc, a ___________________________________ is half of a circle. A ______________________ ___________ is smaller than a semicircle. A ___________________ ______ is greater than a semicircle. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ______________________________ __________ are arcs of the same circle that have exactly _______ ________________ in common! You can add the measures of adjacent arcs just as you can add the measures of adjacent angles! 7-1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The ________________________________ of a circle is the distance around the circle. The number __ ( is the ratio of the circumference of a circle to its diameter. 7-13 Circles that lie in the same plane and have the same center are ___________________________ _________________________. ) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The measure of an arc is in degrees while the ______ ____________________ is a fraction of a circle’s circumference. An arc of 60° represents ___________ or _____________ of the circle. Its arc length is _____ of the circumference of the circle. 7-13 It is possible for two arcs of different circles to have the same measure but different lengths as shown. It is possible for arcs of different circles to have the same length but different measures. ______ _______ are arcs that have the same measure and are in the same circle OR in congruent circles. Name _____________________________________ Class _________ Date ________________ Practice 7-6 Circles and Arcs Find the circumference of each circle. Leave your answers in terms of 1. In 2. C, and . 3. are diameters. Identify the following. 4. two major arcs 5. two minor arcs 6. two semicircles 7. a pair of adjacent arcs 8. an acute central angle 9. an obtuse central angle A market research survey found that adults’ favorite vegetables are as shown below. Find the measure of the central angle for each of the following vegetables. Give your answers to the nearest degree. 10. potatoes 11. green beans 12. corn 13. carrots 14. broccoli Find the measure of each arc in C. 15. 16. 17. 18. 19. 20. Find the length of each arc. Leave your answers in terms of 21. 22. . 23.