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Circle and Polygon Properties

  • Thread starter Turquoise
  • Start date
  • #1
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Homework Statement


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!
 

Answers and Replies

  • #2
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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.
 
  • #3
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What about angle 2 and 3? My answer was 55 for both of them..
 
  • #4
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Those would be correct if triangle BCD is isosceles, with BD = CD. Can you establish that equality somehow?
 
  • #5
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Hmm, I suppose I can't. Now I've hit the bricks, I don't know how to figure it out.
 
  • #6
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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.
 
  • #7
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Once you have angle 4/5 you can easily figure out 2 using inscribed angles and angles formed by tangents.
 
  • #8
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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.
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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