Skills Practice Skills Practice for Lesson.1 Name Date Riding a Ferris Wheel Introduction to ircles Vocabulary Match each definition to its corresponding term. 1. the set of all points equidistant from a point a. arc c. circle 2. the distance from a point on a circle to the center b. central angle i. radius 3. a line segment whose endpoints lie on a circle c. circle d. chord 4. a chord that passes through the center of a circle d. chord e. diameter. a line that intersects a circle at exactly two points e. diameter j. secant 6. a line that intersects a circle at exactly one point f. inscribed angle l. tangent 7. an angle whose vertex is the center of a circle g. major arc b. central angle 8. an angle whose vertex lies on the circle and whose h. minor arc sides are chords of the circle f. inscribed angle 9. an unbroken portion of a circle that lies between i. radius two points on the circle a. arc 10. an arc whose endpoints lie on the diameter j. secant k. semicircle 11. an arc that is less than a semicircle k. semicircle h. minor arc 12. an arc that is greater than a semicircle l. tangent g. major arc hapter l Skills Practice 399
Problem Set Use the given circle to answer each question. 1. a. Name the circle. The name of the circle is circle T. H b. Name each point shown on the circle. The points on the circle are points H, J, K, and L. c. Name the point at the center of the circle. T J The point at the center of the circle is point T. 2. a. Name the circle. The name of the circle is circle X. L K b. Name each point shown on the circle. The points on the circle are points,, and. X c. Name the point at the center of the circle. The point at the center of the circle is point X. 3. Name a radius of circle P. Segment PX is a radius of the circle (also segments PW and PY). W X 4. Name a diameter of circle P. diameter of circle P is chord WY.. Name a chord on circle P that is not a diameter. hord VX is not a diameter. 6. Name a radius of circle. Segment is a radius of the circle (also segments and D). V P Y D E 400 hapter l Skills Practice
Name Date 7. Name a diameter of circle. diameter of circle is chord D. 8. Name a chord on circle that is not a diameter. hord E is not a diameter. 9. Use a straightedge to draw each of the following on circle O. a. chord G b. secant N G M c. tangent MN Sample answers O N 10. Use a straightedge to draw each of the following on circle Y. a. chord LM b. secant LK P c. tangent LP Sample answers L Y M K hapter l Skills Practice 401
Determine whether each angle is an inscribed angle, a central angle, or neither. M J N S P K L 11. MSN 12. MLK central angle inscribed angle 13. KJM 14. NSL neither central angle 1. KMN 16. KPN inscribed angle neither Determine whether each arc is a semicircle, a minor arc, or a major arc. R D 17. D 18. D semicircle minor arc 19. D 20. major arc semicircle 21. 22. D minor arc major arc 402 hapter l Skills Practice
Skills Practice Skills Practice for Lesson.2 Name Date Holding the Wheel entral ngles, Inscribed ngles, and Intercepted rcs Vocabulary Use the diagram of circle P to answer Questions 1 through 4. P D 1. Name all of the central angles in the diagram. P, P, PD, DP 2. Name all of the inscribed angles in the diagram., D 3. Name all of the minor arcs in the diagram.,, D, D 4. Name all of the intercepted arcs in the diagram., D. Describe how to calculate the measure of a minor arc if you know the measure of its central angle. The measure of a minor arc is equal to the measure of its central angle. 6. Describe how to calculate the measure of an inscribed angle if you know the measure of its central angle. The measure of an inscribed angle is equal to half the measure of its central angle. hapter l Skills Practice 403
Problem Set Use the given information to determine the measure of the indicated arc. 1. mt 36 2. mmd 113 m 36 md 113 T M D 3. mfzg 90 4. mjvk 9 mfg 90 mjk 9 J Z F G V K Use the given information to determine the measure of the indicated angle.. m 46 6. muv 19. m 46 muwv W U V 7. mmn 140. 8. mhk 161 19. mmqn 140. mhnk 161 M N H Q N K 404 hapter l Skills Practice
Name Date Use the given information to determine the measure of the indicated arc. 9. mdef 84 10. mpqr 31 mdf 168 mpr 62 D Q E O F P R 11. mwxy 19 12. mjkl. mwy 38 m JL 111 W Y P X J L K Use the given information to determine the measure of the indicated angle. 13. myz 28 14. mlk 87 myxz 14 mlmk 43. L K Y X O N Z M 1. mqr 16 16. mst 102 mqpr 82. mswt 1 P S W Q T R T hapter l Skills Practice 40
406 hapter l Skills Practice
Skills Practice Skills Practice for Lesson.3 Name Date Manhole overs Measuring ngles Inside and Outside of ircles Vocabulary Match each diagram to the term that best describes it. 1. 2. a. central angle b. chord c. diameter d. inscribed angle c. diameter d. inscribed angle 3. 4. e. secant f. tangent a. central angle b. chord. 6. f. tangent e. secant hapter l Skills Practice 407
Problem Set Use the given information to determine the measure of the indicated central or inscribed angle. 1. 2. X K D m 40º md 120º mx 40 mkd 120 3. 4. N L D m 40º md 120º ml 20 mnd 60 408 hapter l Skills Practice
Name Date Use the given arc measures to determine the measure of the indicated angle.. L 6. P O R N M S X Q mlm 90º mon 36º mlrm 63 R mps 170º mqr 28º mpxs 99 mnrm mlrm 1 (mlm mon) 2 mlrm 1 (90º 36º) 2 mlrm 1 2 (126º) mlrm 63º 117 msxr mpxs 1 (mps mqr) 2 mpxs 1 (170º 28º) 2 mpxs 1 2 (198º) mpxs 99º 81 mnrm 180º 63º msxr 180º 99º 117º 81º hapter l Skills Practice 409
7. 8. X V Y Z D E med 140º md 10º med 1 W mxy 20º myz 0º md 2 mxvy 7 ecause arc D is a semicircle, its measure is 180º. md m md 180º m 10º m 170º med 1 (med m) 2 med 1 (140º 170º) 2 med 1 2 (310º) med 1º md 180º 1º 2º myvz 10 ecause arc YZW is a semicircle, its measure is 180º. myzw myz mzw 180º 0º mzw mzw 130º mxvy 1 (mxy mzw ) 2 mxvy 1 (20º 130º) 2 mxvy 1 2 (10º) mxvy 7º myvz 180º 7º 10º 410 hapter l Skills Practice
Name Date 9. 10. E H I J D L me 20º mjk 164º md 70º m I L 42º K m 2 mh 61 m 1 (md me ) mh 1 2 2 (mjk m I L ) m 1 (70º 20º) mh 1 (164º 42º) 2 2 m 1 (0º) mh 1 2 2 (122º) m 2º mh 61º 11. 12. M D Q N P O E me 170º mmq 0º md 20º mnp 12º m 7 mo m 1 (me md) mo 1 (mmq mnp) 2 2 m 1 (170º 20º) mo 1 (0º 12º) 2 2 19 m 1 (10º) mo 1 2 2 (38º) m 7º mo 19º hapter l Skills Practice 411
13. 14. L X O P Q ml 108º mxp 120º ml 4 mxpo 60 ml 1 (ml) mxpo 1 2 2 (mxp) ml 1 (108º) mxpo 1 2 2 (120º) ml 4º mxpo 60º Use the given angle measures to determine the degree measure of the indicated arc. 1. 16. H G F mgf 70º mf 20º mg F 140 mf 40 mgf 1 (mg) mf 1 2 2 (mf ) 70º 1 (mg) 20º 1 2 2 (mf ) 140º mg 40º mf 412 hapter l Skills Practice
Name Date 17. 18. N L M Q P V W Y Z X mnq 160º mwy 10º ml 40º mv 10º mmq 80 mxy 30 ml 1 (mnq mmq) mv 1 (mxy mwy ) 2 2 40º 1 (160º mmq) 10º 1 (mxy 10º) 2 2 80º 160º mmq 20º mxy 10º 80º mmq 30º mxy mmq 80º hapter l Skills Practice 413
Use the given arc measures to determine the measure of the indicated angle. 19. 20. G H D F I md 228º mgfi 24º md 132º mg I 106º m 48 mh 74 m 1 (md md) mh 1 (mgfi mg I ) 2 2 m 1 (228º 132º) mh 1 (24º 106º) 2 2 m 1 (96º) mh 1 2 2 (148º) m 48º mh 74º 414 hapter l Skills Practice
Name Date 21. 22. S J K L P R M Q mpsr 23º mjml 309º mpr 12º mjl 1º mq mk 129 mq 1 (mpsr mpr) mk 1 (mjml mjl ) 2 2 mq 1 (23º 12º) mk 1 (309º 1º) 2 2 mq 1 (110º) mk 1 2 2 (28º) mq º mk 129º hapter l Skills Practice 41
416 hapter l Skills Practice
Skills Practice Skills Practice for Lesson.4 Name Date olor Theory hords and ircles Vocabulary 1. Describe how to use two chords to find the center of a circle. To use two chords to find the center of a circle, find the perpendicular bisector of each chord. The intersection of the perpendicular bisectors is the center of the circle. 2. an the perpendicular bisectors of parallel chords be used to find the center of a circle? Why or why not? The perpendicular bisectors of parallel chords cannot be used to find the center of a circle. The perpendicular bisectors of the chords are the same line or line segment. 3. Describe how the minor arcs of congruent chords are related. The minor arcs of congruent chords are congruent. If two minor arcs in a circle are congruent, then their corresponding chords are congruent. 4. Define perpendicular bisector in your own words. perpendicular bisector is a line or line segment that is perpendicular to a segment at its midpoint. Problem Set Use the diagram and your understanding of perpendicular bisectors to complete each statement. G X R D H 1. D 3. SH RH 2. D 4. RM _ SM _ M S hapter l Skills Practice 417
Use a compass and straightedge to draw the perpendicular bisector of each chord.. 6. 7. 8. Use the diagram and your understanding of congruency to complete each statement. L Y O X N M 9. X X LO MN LO MN _ L O _ M _ N _ X U S V W 10. US VS XZ YW XZ YW _ XU ZU YV WV _ Z 418 hapter l Skills Practice
Name Date Q P D R S F L G M K N J 11. D PR QS _ PR QS P R QD SD 12. LM NM _ GF KJ GF KJ GL FL _ KN JN Locate the center of each circle using the given chords. 13. 14. 1. 16. hapter l Skills Practice 419
Skills Practice Skills Practice for Lesson. Name Date Solar Eclipses Tangents and ircles Vocabulary 1. Describe how the three terms tangent line, point of tangency, and tangent segment are related. Identify similarities and differences. tangent line is a line that intersects a circle at exactly one point. That point is called the point of tangency. tangent segment is a segment of a tangent line. One endpoint of the tangent segment is the point of tangency. ll three terms involve one point on a circle. The point of tangency is one point that is on the circle. 2. Describe how the terms tangent and radius are related. Identify similarities and differences. oth the terms tangent and radius are related to circles. circle has an infinite number of tangents and radii. tangent intersects a circle at exactly one point. The remaining points on a tangent are on the exterior of a circle. radius intersects a circle at exactly one point. The remaining points on a radius are on the interior of the circle, and end at the center. tangent to a circle is perpendicular to the radius that is drawn from the point of tangency. Problem Set Draw the indicated segment or line for each circle. 1. tangent D D 2. tangent XZ X O Z hapter l Skills Practice 421
3. radius DK 4. radius PT K T D P Use a straight edge to draw a congruent tangent segment for each given tangent segment.. 6. 7. 8. 422 hapter l Skills Practice
Name Date Use the given measurements to determine the measure of each indicated angle. 9. 10. R X T D S mrxs 34º m 70º mxrs 73º m º mrsx 73º m º 2(mXRS) mrxs 180º 2(m) m 180º 2(mXRS) 34º 180º 2(m) 70º 180º 2(mXRS) 146º 2(m) 110º mxrs 73º m º mxrs mrsx m m 11. 12. M O J N X Y K momn 42º mljk 80º monm 42º mjkl 80º L mmon 96º mjlk 20º momn monm 42º mljk mjkl 80º momn monm mmon 180º mljk mjkl mjlk 180º 42º 42º mmon 180º 80º 80º mjlk 180º 84º mmon 180º 160º mjlk 180º mmon 96º mjlk 20º hapter l Skills Practice 423
13. Line is tangent to circle O. mo 120º mo 90º mo 30º mo 60º mo 90º mo mo 120º 90º mo 120º mo 30º mo mo 180º mo 120º 180º mo 180º 120º mo 60º 14. Line RU is tangent to circle S. mqrs 142º msur 90º O msru 38º S Q mrsu 2º R msur 90º msru mqrs 180º msru 142º 180º msru 38º mrsu 180º msur msru mrsu 180º 90º 38º U mrsu 2º 424 hapter l Skills Practice
Skills Practice Skills Practice for Lesson.6 Name Date Gears rc Length Vocabulary Define each term in your own words. 1. arc n arc is an unbroken portion of a circle that lies between two points on the circle. 2. measure of a minor arc The measure of a minor arc is the degree measure of its central angle. 3. arc length rc length is the measure of the length in linear units, such as inches or centimeters. It is a portion of the circumference. Problem Set Determine the measure of each minor arc. 1. M L 40 4 in. T 2. Z 10 m mlm 40º m 100º 100 hapter l Skills Practice 42
3. 4. O 36 8 cm D 140 1 in. F E S T mst 36º med 140º. M 6. J 3 m 20 m 20 K O 120 R N mmn 120º mjk 20º 7. 8. cm 80 2 ft 0 m 80º m 0º alculate the circumference for each circle. Write your answers in terms of. 9. 10. 0 cm 19 in. 2r 2(0) 100 centimeters 2r 2(19) 38 inches 426 hapter l Skills Practice
Name Date 11. 12. 10. ft 4.2 m 2r 2(10.) 21 feet 2r 2(4.2) 8.4 meters alculate the arc length of the minor arc in each circle. Write your answers in terms of. 13. L 14. M 40 4 in. T Z 10 m 100 1. rc length of LM: ( mlm 360 ) 2r ( 40 360 ) 2(4) ( m S O 36 ( 1 rc length of : 360 ) 2r ( 100 360 ) 2(10) 9 ) 8 ( 18 ) 20 8 inches 0 9 9 meters 8 cm T 16. D 140 1 in. F E rc length of ST: ( mst 360 ) 2r ( 36 360 ) 2(8) ( mde ( 1 rc length of DE: 360 ) 2r ( 140 360 ) 2(1) 18 ) 30 _ 210 18 10 ) 16 ( 7 8 centimeters 3 3 inches hapter l Skills Practice 427
17. M 18. J 3 m 20 m 20 K O 120 R N rc length of MN: ( mmn 360 ) 2r ( 120 360 ) 2(3) ( mjk ( 1 19. rc length of JK: 360 ) 2r ( 20 360 ) 2(20) 3 ) 6 ( 1 18 ) 40 2 meters 20 9 meters 20. cm 80 2 ft 0 rc length of : ( m 360 ) 2r ( 80 360 ) 2() ( m ( 2 rc length of : 360 ) 2r ( 0 360 ) 2(2) 9 ) 10 ( 36 ) 4 20 9 centimeters 9 feet 428 hapter l Skills Practice
Skills Practice Skills Practice for Lesson.7 Name Date Playing Darts reas of Parts of ircles Vocabulary Provide an example of each of the following. Use words and diagrams as necessary. 1. concentric circles 2. sector of circle sector of circle The two circles have the same center. 3. segment of circle segment of circle hapter l Skills Practice 429
Problem Set List the names of the radii and the arc that is intercepted by the radii that form each sector. 1. W X 2. P D radius: PW _ radius: PX arc: WX radius: radius: D arc: D 3. J 4. Q G K R Z radius: GJ _ radius: QR radius: GK radius: QZ arc: JK arc: RZ alculate the area of each circle. Use 3.14 for.. 6. L T 4 in. 9 cm r 2 r 2 (4) 2 (9) 2 3.14(16) 3.14(81) 0.24 square inches 24.34 square centimeters 430 hapter l Skills Practice
Name Date 7. 8. 6. mm 18.4 ft r 2 r 2 (6.) 2 (18.4) 2 3.14(42.2) 3.14(338.6) 132.66 square millimeters 1063.0784 square feet alculate the area of each sector. Use 3.14 for. Round to the nearest hundredth, if necessary. 9. 10. D O 3 cm 40 120 F 2 in. E _ 40 360 r2 _ 120 360 r2 1 9 (3)2 1 3 (2)2 1 9 (9) 1 3 (3.14)(4) 3.14 square centimeters 4.19 square inches hapter l Skills Practice 431
11. 0. m S R 160 12. 10 cm 20 _ 160 360 r2 _ 20 360 r2 4 9 (0.)2 1 18 (10)2 4 9 (3.14)(0.2) 1 18 (3.14)(100) 0.3 square meters 17.44 square centimeters 13. 14. 6 cm 80 D 2 ft 0 E _ 80 360 r2 _ 0 360 r2 2 9 (6)2 36 (2)2 2 9 (3.14)(36) 36 (3.14)(4) 2.12 square centimeters F 1.74 square feet 432 hapter l Skills Practice
Name Date alculate the area of the indicated triangle. Round to the nearest hundredth, if necessary. 1. 3 in rea of 4. square inches rea of 1 2 bh 1 2 (3)(3) 9 4. square inches 2 16. J 16 m L K rea of JKL 128 square meters rea of JKL 1 2 bh 1 2 (16)(16) _ 26 128 square meters 2 hapter l Skills Practice 433
17. X 2 cm 60 Z Y rea of XYZ 3 1.73 square centimeters XYZ is an equilateral triangle, so the base is 2 centimetres, and the height is 3 centimeters. rea of XYZ 1 2 bh 1 2 (2)( 3 ) 3 1.73 square centimeters 18. Q ft 60 R S rea of QRS 6.2 3 10.83 square feet QRS is an equilateral triangle, so the base is feet, and the height is 2. 3 feet. rea of QRS 1 2 bh 1 2 ()(2. 3 ) 6.2 3 10.83 square feet 434 hapter l Skills Practice
Name Date alculate the area of the shaded segment of the circle. 19. 3 in. The area of the shaded segment the area of sector the area of triangle. rea of sector 90 _ 360 r2 rea of 1 2 bh 1 2 (3)(3) 1 4 (3)2 1 4 (3.14)(9) 7.07 square inches 9 4. square inches 2 rea of segment 7.07 4. 2.7 square inches hapter l Skills Practice 43
20. 12 in. O M The area of the shaded segment the area of sector MO the area of triangle MO. rea of sector MO 90 _ 360 r2 rea of MO 1 2 bh 1 4 (12)2 1 4 (3.14)(144) 113.04 square inches 1 2 (12)(12) 72 square inches rea of segment 113.04 72 41.04 square inches 436 hapter l Skills Practice
Name Date 21. X 2 cm 60 Z Y The area of the shaded segment the area of sector XYZ the area of triangle XYZ. rea of sector XYZ r 2 _ 60 360 (2)2 1 6 (3.14)(4) 2.09 square centimeters XYZ is an equilateral triangle, so the base is 2 centimeters and the height is 3 centimeters. rea of XYZ 1 2 bh 1 2 (2)( 3 ) 3 1.73 square centimeters rea of segment 2.09 1.73 0.36 square centimeters hapter l Skills Practice 437
22. Q 6 cm 60 P R The area of the shaded segment the area of sector PQR the area of triangle PQR. rea of sector PQR 60 _ 360 r2 _ 60 360 (6)2 1 6 (3.14)(36) 18.84 square centimeters PQR is an equilateral triangle, so the base is 6 centimeters and the height is 3 3 centimeters. rea of XYZ 1 2 bh 1 2 (6)(3 3 ) 1.9 square centimeters rea of segment 18.84 1.9 3.2 square centimeters 438 hapter l Skills Practice
Skills Practice Skills Practice for Lesson.8 Name Date rop ircles ircle Measurements and Relationships Vocabulary Write the term that best completes each statement. 1. ircles that share the same center but have different radii lengths are called concentric. 2. rc length is measured in linear units. 3. When an arc measure is 180º, the arc is called a semicircle. 4. central angle is equal to the measure of its intercepted arc.. circle segment is bounded by an arc and the line segment that intercepts the arc endpoints. 6. tangent to a circle is perpendicular to the radius that is drawn from the point of tangency. Problem Set Use the given information to determine the measure of the indicated central or inscribed angle. 1. 2. R N L m = 60º mlr = 110º m = 60º mlnr = 110º hapter l Skills Practice 439
3. M L 4. Y Z N X mln = 48º mxz = 170º mlmn = 24º mxyz = 8º alculate the area of each sector. Use 3.14 for.. Find the area of the sector of a circle with a radius of 4 meters formed by a central angle of 4º. 4 _ 360 r2 1 8 (4)2 ( 1 8 ) (3.14)(16) 6.28 square meters 6. Find the area of the sector of a circle with a radius of 12 meters formed by a central angle of 30º. _ 30 360 r2 1 12 (12)2 ( 1 12 ) (3.14)(144) 37.68 square meters 7. Find the area of the sector of a circle with a radius of 22 inches formed by a central angle of 60. 60 _ 360 r2 1 6 (22)2 ( 1 6 ) (3.14)(484) 23.29 square inches 440 hapter l Skills Practice
8. Find the area of the sector of a circle with a radius of 0 inches formed by a central angle of 40. 40 _ 360 r2 1 9 (0)2 ( 1 9 ) (3.14)(200) 872.22 square inches alculate the length of each arc. Leave your answers in terms of. 9. Find the length of an arc of a circle with a radius of 16 centimeters formed by a central angle of 60º. arc length 60 _ 360 2r arc length 1 6 2(16) arc length 16 3 centimeters 10. Find the length of an arc of a circle with a radius of 30 centimeters formed by a central angle of 40º. arc length 40 _ 360 2r arc length 1 9 2(30) arc length 20 3 centimeters 11. Find the length of an arc of a circle with a radius of 9 feet formed by a central angle of 0. arc length 0 _ 360 2r arc length 36 2(9) arc length 2 feet 12. Find the length of an arc of a circle with a radius of 62 feet formed by a central angle of 7. arc length 7 _ 360 2r arc length 24 2(62) arc length 1 _ 6 feet hapter l Skills Practice 441
nswer each question using the given measurements. Use 3.14 for. Round to the nearest hundredth, if necessary. 13. 6-inch long pendulum swings through an angle of 90º every second. How far does the tip of the pendulum move each second? arc length 90 _ 360 2r arc length ( 1 4 ) 2(6) arc length 3 9.42 inches The tip of the pendulum moves about 9.42 inches each second. 14. The minute-hand on a clock is 4 inches long. How far does the tip of the minute-hand move in 2 minutes? In 2 minutes, the minute-hand on a clock moves 2 60, or 12 the face, or 10º. arc length 10 _ 360 2r arc length ( 12 ) 2(4) of the way around arc length 10 10.47 inches 3 The tip of the minute-hand moves about 10.47 inches in 2 minutes. 442 hapter l Skills Practice
Name Date 1. water sprinkler sprays water a distance of 30 feet. It rotates through a 120º angle. What area of the lawn receives water? 120 30 ft The area receiving water is a sector of a circle. 120 _ 360 r2 1 3 (30)2 ( 1 3 ) (3.14)(900) 942 square feet bout 942 square feet of lawn receives water from the sprinkler. 16. semicircular silk fan has a radius of 10 inches. Not including any overlap for seams or edges, how much silk is used for the fan? 10 inches The fan is a sector of a circle, with an angle of 180º. 180 _ 360 r2 1 2 (10)2 ( 1 2 ) (3.14)(100) 17 square inches bout 17 square inches of silk is used for the fan. hapter l Skills Practice 443
Use the given information to determine the measure of each arc. 17. 18. P T R S X D E msxr 40º md 0º msr 20º md 68º mpt 100º me 32º msxr ( 1 2 ) (mpt msr) md ( 1 2 )(m D me ) 40º ( 1 2 ) (mpt 20º) 0º ( 1 2 )(68º me ) 80º mpt 20º 100º 68º me 100º mpt 32º me 19. 20. X G J W Y F H K mghf 60º mwxy 70º mgf 32º mwy 28º mjk 88º mvz 168º mghf 1 (mgf mjk ) mwxy 1 (mvz mwy ) 2 2 60º 1 (32º mjk ) 70º 1 (mvz 28º ) 2 2 120º 32º mjk 140º mvz 28º 88º mjk 168º mvz V Z 444 hapter l Skills Practice