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Home > CCG > Chapter 10 > Lesson 10.1.3 > Problem 10-32

10-32.

A circle, with center, P, has points C, and D, A smaller circle, inside, also with center, P, has points, A, & B, placed so that line segment, P, C, passes through, A, and line segment, P, D, passes through, B.The figure at right shows two concentric circles.  

 

  1. What is the relationship between and ? How do you know?

    They are similar. Both are the intercepted arc of central angle .

  2. Which has greater measure, or ? Which has greater length? Explain.

    We already know that both share the same central angle. Which one has a larger radius?

    Both arcs have the same measure.

     has greater length.

  3. If and , find the length of . Show all work.

    Arc is a fraction of a circle with a radius of and a circumference of .

    Therefore, the length of .