46. Time Hands of a clock suggest an angle whose measure is continually changing. How many degrees does a minute hand move through during each time interval?
    1. 1 min
    2. 5 min
    3. 20 min

Algebra Find the value of each variable.

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49. Landscape Design A landscape architect is constructing a curved path through a rectangular yard. The curved path consists of two 90 ° 90 degrees  arcs. He plans to edge the two sides of the path with plastic edging. What is the total length of plastic edging he will need? Round your answer to the nearest meter.

    

50. Reasoning Suppose the radius of a circle is doubled. How does this affect the circumference of the circle? Explain.
51. A 60 ° 60 degrees  arc of ⊙ A circle dot eh  has the same length as a 45 ° 45 degrees  arc of ⊙ B . circle dot b .  What is the ratio of the radius of ⊙ A circle dot eh  to the radius of ⊙ B ? circle dot b question mark

Find the length of each arc shown in red. Leave your answer in terms of π . pi .

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55. Coordinate Geometry Find the length of a semicircle with endpoints (1, 3) and (4, 7). Round your answer to the nearest tenth.
56. In ⊙ O circle dot o , the length of A B ⌢ modified eh b with frown above  is 6 π 6 pi  cm and m A B ⌢ m , modified eh b with frown above  is 120. What is the diameter of ⊙ O ? circle dot o question mark

C Challenge

57. The diagram below shows two concentric circles. A R ¯ ≅ R W ¯ . eh r bar , approximately equal to . r w bar , .  Show that the length of S T ⌢ modified s t with frown above  is equal to the length of Q R ⌢ . modified q r with frown above , .

    

58. Proof Given: ⊙ P circle dot p  with A B ¯ | | P C ¯ eh b bar , vertical line vertical line , p c bar

    Prove: m B C ⌢ = m C D ⌢ m , modified b c with frown above . equals m . modified c d with frown above

    

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