If the measure ofaacb is less than 180, then A, B, and all the points on C that lie in the

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1 age 1 of rcs and entral ngles oal Use properties of arcs of circles. Key Words minor arc major arc semicircle congruent circles congruent arcs arc length ny two points and on a circle determine a minor arc and a major arc (unless the points lie on a diameter). If the measure ofa is less than 180, then,, and all the points on that lie in the interior of a form a minor arc. oints,, and all the points on that do not lie on s form a major arc. You name an arc by its endpoints. Use one other point on a major arc as part of its name to distinguish it from the minor arc. minor arc r major arc t Student elp LOOK K or the definition of a central angle, see p. 5. The measures of a minor arc and a major arc depend on the central angle of the minor arc. m r The measure of a minor arc is the measure of its central angle. The measure of a major arc is the difference of 3 and the measure of the related minor arc. m t semicircle is an arc whose central angle measures 180. semicircle is named by three points. Its measure is 180. XML 1 Name and ind Measures of rcs Name the red arc and identify the type of arc. Then find its measure. a. b. L K 110 M N a. s is a minor arc. Its measure is. b. LMN t is a major arc. Its measure is rcs and entral ngles 601

2 age 2 of 7 Visualize It! OSTULT 16 rc ddition ostulate Words The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. rcs of a circle are adjacent if they intersect only at their endpoints. r and r are adjacent. Symbols m t ms ms XML 2 ind Measures of rcs ind the measure of t. m t mt mt ms Two circles are congruent circles if they have the same radius. Two arcs of the same circle or of congruent circles are congruent arcs if they have the same measure. XML 3 Identify ongruent rcs ind the measures of the blue arcs. re the arcs congruent? a. b. Z X Y W a. Notice that s and s are in the same circle. ecause ms ms 5, scs. b. Notice that XYs and ZWs are not in the same circle or in congruent circles. Therefore, although mxys mzws 65, XYsçZWs. Identify ongruent rcs ind the measures of the arcs. re the arcs congruent? 1. s and s 2. s and s s and s. t and t 602 hapter 11 ircles

3 age 3 of 7 Student elp SKILLS VIW To review finding circumference of a circle, see p. 67. rc Length n arc length is a portion of the circumference of a circle. You can write a proportion to find arc length. arc length central angle r arc len g 2π th of r r m r 36 0 full circumference full circle LNT Words In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 3. Symbols rc length of s m 36 r p2πr 0 r XML ind rc Lengths ind the length of the red arc. a. b. c. 5 cm 7 cm 7 cm 98 Student elp STUY TI You can substitute 3.1 as an approimation of π or use a calculator. a. rc length of s p2π(5).36 centimeters 3 b. rc length of s p2π(7) 6.11 centimeters 3 98 c. rc length of s p2π(7) centimeters 3 ind rc Lengths ind the length of the red arc. ound your answer to the nearest hundredth N 2 in ft M 90 6 cm 11.3 rcs and entral ngles 603

4 age of ercises uided ractice Vocabulary heck 1. In the diagram at the right, identify a major arc, a minor arc, and a semicircle. 2. raw a circle with a pair of congruent arcs. 3. What is the difference between arc measure and arc length? Skill heck ind the measure in T.. msr 5. ms t 6. mq t 8. mqs t 7. mqs r 9. maqt 120 T S ind the blue arc length. ound your answer to the nearest hundredth. 10. Length of s 11. Length of s 12. Length of t 2 yd 6 cm m 1 ractice and pplications tra ractice See p Naming rcs Name the blue minor arc and find its measure L 1 N omework elp ample 1: s ample 2: s ample 3: s. 3 6 ample : s hapter 11 ircles Naming rcs Name the blue major arc and find its measure W X 1 Y 30

5 age 5 of 7 Types of rcs etermine whether the arc is a minor arc, a major arc, or a semicircle of. T &* and QU &** are diameters. 19. Qr 20. SUs 21. QT t 23. TUQ t 25. QUT t 22. QTs 2. TU t 26. UQ t U T S inding the entral ngle ind the measure of a Student elp VISUL STTY In s , copy the diagram and add information to it as you solve the eercises, as shown on p Measuring rcs and entral ngles KN&* and JL&* are diameters. ind the measure. 30. mkl r 32. mlnk t 3. mnjk t 36. mml r 31. mmnt 33. mmkn t 35. mamql 37. majqn 38. mjmr 39. mlns N M J 55 L K Time Zone Wheel In ercises 0 2, use the following information. To find the time in Tokyo when it is.m. in San rancisco, rotate the small wheel until.m. and San rancisco line up as shown. Then look at Tokyo to see that it is 9.M. there. When it is 9.M. in Tokyo Tokyo Manila angkok 10 Sydney 11 Nouméa Noon 12 Wellington 1 nadyr onolulu nchorage San rancisco 2 enver it is.m. in San rancisco.m. 6 5 Tashkent Karachi 3 Seychelles Moscow 2 elsinki ome 1 ernando de Noronha reenwich 12 zores Midnight 11 New Orleans oston aracas odthab M What is the arc measure for each time zone on the wheel? 1. What is the measure of the minor arc from the Tokyo zone to the nchorage zone? 2. If two cities differ by 180 on the wheel, then it is 3:00.M. in one city when it is? in the other city rcs and entral ngles 605

6 age 6 of 7 IStudent elp I L S S Z O N. O M OMWOK L tra help with problem solving in s is at classzone.com Naming ongruent rcs re the blue arcs congruent? plain. 3. J. L K T U W X Z Y J K inding rc Length ind the length of r. ound your answer to the nearest hundredth cm 7 in ft m 75 cm 1 6 in. You be the Judge 53. friend tells you two arcs from different circles have the same arc length if their central angles are equal. Is your friend correct? plain your reasoning. 5. hallenge ngineers reduced the lean of the Leaning Tower of isa. If they moved it back 0.6, what was the arc length of the move? ound your answer to the nearest whole number cm 606 hapter 11 ircles

7 age 7 of 7 Standardized Test ractice Mied eview lgebra Skills 55. Multiple hoice What is the length of s in shown below? 5.6 ft 19.5 ft 16.8 ft 25.1 ft inding Leg Lengths ind the lengths of the legs of the triangle. ound your answers to the nearest tenth. (Lesson 10.5) y y Simplifying atios Simplify the ratio. (Skills eview, p. 660) 2 km 5 ft yards ounces km 7 2 in. 27 ft 8 pounds 8 ft 8 1 y Quiz 1 Tell whether the given line, segment, or point is best described as a chord, a secant, a tangent, a diameter, a radius, or a point of tangency. (Lesson 11.1) 1. ^&*( 2. ^&*( J J 3. &* 5. &*. J&* 6. Q&* and &* are tangent to. ind the value of. (Lesson 11.2) ind the length of s. ound your answer to the nearest hundredth. (Lesson 11.3) cm 1 7 m 10 ft rcs and entral ngles 607