Name LESSON 10.1 State the best term for the given figure in the diagram. 9. Find the diameter and radius of A, B, and C. 10. Describe the point of intersection of all three circles. 11. Describe all the common tangents of A and B. 12. Describe the common secant of A and C that passes through both intersections of the two circles. Draw a pair of circles with the characteristics described. 13. non-intersecting circles, no common tangents 1. F 2. FE 3. HG 4. DB 5. C 6. BE 7. DB 14. intersecting circles, 2 common tangents 15. 1 point of intersection, 1 common tangent 8. AG Use the diagram below for 9-12. 16. 1 point of intersection, 3 common tangents
In the diagram, segment BC is a radius of C. Determine whether segment AB is tangent to C. Explain your reasoning.! 17. 22. 18. 23. 24. 19. In the diagram, assume that segments are tangents if they appear to be. Find the value(s) of x. 20. 25. Water Tank You are standing 14 feet from the edge of a cylindrical water tank and 26 feet from a point of tangency. The tank is 10 feet tall. What is the volume of the tank in cubic feet? 21.
27. Pulleys The figure shows a pulley system in which a belt is wrapped around two pulleys so that one can drive the other. segment US is tangent to Q at R and to P at S. Segment QT is perpendicular to segment PS, and Q and P are the centers of the circles. Let QR = 2 in., PS = 8 in., and PQ = 12 in. a) Find RS. b) Find m angle QPT Find the indicated are measure. 10. m QS 11. m LKJ! 12. m DH LESSON 10.2 NR and MQ are diameters of O. Determine whether the given arc is a minor arc, major arc, or semicircle. Then find the measure of the arc. 1. MQN 2. NQ 3. QR 4. QMR 5. MR 6. MRQ 7. NQR 8. MN 9. QR RS Find the value of x 13. 14. 15.
AC and BD are diameters of E. Find the measure of the given arc if m ACD = 316. 16. m AD 17. m BC 18. m BCA 19. m DCB In Exercises 28-32, use the following information. Game Timer The device shown is a 10-second game timer. The top plunger button alternatively stops and starts the timer. For game play, the timer is started at 10 (as shown) and moves counterclockwise. Players often start and stop the timer several times before it reaches 0. Give all answers to the nearest tenth. RT and PS are diameters of N. Find the measure of the given arc if m TP = 47. 20. m PR 21. m RTP 22. m STR 23. m ST Tell whether AB CD. Explain. 24. 28. What is the measure of the arc traced out by the tip of the pointer as it moves from one number to the next on the timer? 29. What is the measure of the arc traced out as the pointer moves from the 10 to the 0? 30. A player starts the timer at the 10 and stops it after 3.4 seconds. What is the measure of the arc generated? 31. A player stops the timer after 2.3 seconds, then after 1.2 seconds, and again after 2.5 seconds. What is the sum of the measures of the arcs? 32. How much time does it take the pointer to trace out an arc of 60? 25. 26. LESSON 10.3 What can you conclude about the diagram? State a postulate or theorem that justifies your answer. 1. 27. 2.
P is the center of the circle. Use the given information to find XY. 3. ZY = 3 7. 8. 4. ZY = 6, XW = 4 9. 5. CA = 3 10. 11. Find the measure of MN. 6.
12. 24. Pool You challenge a friend to find a way to use three 10-foot boards to mark the location of the center of a circular swimming pool with a diameter of 12 feet. Your friend centers the top board on the other two boards and makes sure its ends are the same distance from the edge of the pool as shown at the right. Then your friend marks a spot on the exact center of the top board. Is this the center of the pool? Explain. 13. 14. Use the figure to match the chord or arc with a congruent arc or chord. 16. DC A. FE 17. PD B. ED 18. EC C. EC 19. BC D. AB 20. AF E. BF 21. FB F. PA LESSON 10.4 Find the indicated measure. 1. m BC 2. m AB
3. m BC 8. m B 4. m A 9. m ABC 5. m C 6. m AD Find the indicated measure in O, given m arc CD = 85 and m arc BE = 97. 10. m ABC 11. m CED 12. m BDE 13. m CBD 14. m ABD 15. m BCE 7. m BC
LESSON 10.5 Find the value(s) of the variable(s). 16. Find the measure of 1. 1. 17. 2. 18. 3. 19. 4. 20. 5. 21. 6.
Use the information given in the diagram to find the measure. 7. m TV 8. m SV 9. m STU 10. m VWU LESSON 10.6 Find the value of x. Round decimal answers to the nearest tenth. 1. 2. Find the value of x. 11. 3. 12. 4. 13. 5. 14. 6.
7. 12. In the figure at the below, let AP = x, PQ = x + 2, QB = x + 4, CP = 2, PD = 6x, EQ = y, and QD = 14. Find all the unknown segment lengths. 8. 9. 11. Can Theorem 10.14 be used to solve for x and y in the concentric circles below? Explain why or why not. 13. Water Tank You want to estimate the diameter of a circular water tank. You stand at a location 10.5 feet from the edge of the circular tank. From this position, your distance to a point of tangency on the tank is 23 feet. a. Draw a diagram of the situation. Label your position as C and the radius of the tank as r. b. Find the length of the radius to the nearest tenth of a foot. 14. Satellite A satellite is about 100 miles above Earth s surface. The satellite is taking photographs of Earth. Earth s diameter is about 8000 miles. What is the distance from the satellite to a point of tangency from the satellite to Earth? a. Draw a diagram of the situation, representing Earth as a circle. b. In the diagram, draw a segment to show one of the farthest possible points on Earth that can be photographed from the satellite. What type of geometric figure is the segment? c. Find the length of the segment drawn in part (b).