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Circle and Polygon Properties

  1. Apr 27, 2009 #1
    1. The problem statement, all variables and given/known data
    http://i41.tinypic.com/35mno6v.jpg


    2. The attempt at a solution
    So far, I found out that angle 4 and 5 is 55, because angle D is 110.. but I don't know if that's right. Please help!
     
  2. jcsd
  3. Apr 27, 2009 #2

    Mark44

    Staff: Mentor

    Angle BDA is 110 degrees, because angle 1 is 70 degrees. Angles 4 and 5 are equal, because triangle BDA is isosceles. Angles 4, 5 and BDA have to add to 180 degrees, which they don't do if angles 4 and 5 are 55 degrees each.
     
  4. Apr 27, 2009 #3
    What about angle 2 and 3? My answer was 55 for both of them..
     
  5. Apr 27, 2009 #4

    Mark44

    Staff: Mentor

    Those would be correct if triangle BCD is isosceles, with BD = CD. Can you establish that equality somehow?
     
  6. Apr 27, 2009 #5
    Hmm, I suppose I can't. Now I've hit the bricks, I don't know how to figure it out.
     
  7. Apr 28, 2009 #6

    Mark44

    Staff: Mentor

    Is there any other information given in this problem, such as at the top of the set of problems?

    One thing I haven't used is the statement that AB is tangent at B. I don't understand why this is significant or how it ties into this problem.
     
  8. Apr 30, 2009 #7
    Once you have angle 4/5 you can easily figure out 2 using inscribed angles and angles formed by tangents.
     
  9. May 4, 2009 #8
    It is significant because an angle formed by a chord and a tangent to a circle is half the arc it intercepts. Angles 2 and 4 are inscribed angles that intercept the same arc, so they are congruent.
     
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