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Geometry Proof (Circles and Chords)

  1. Oct 15, 2011 #1
    Hey all. At my school we have these things called "Real Problems" that we get every 3-4 weeks. This time it's about proofs. I have an A- in the class, so I got the difficult one with 4 very difficult (IMO) proofs.

    I have NO idea where to start on this..I have drawn it out for you. All help is greatly appreciated. I am here to merely learn, not copy everything. I would appreciate full answers, but I am definitely here to Learn how to do this for tests.

    Given: Tangent line AB and chord BC.
    Prove: <ABC = (1/2)(arc)BC

    In other words prove: (Angle ABC = Half of arc BC)

    HINT: Using the center of the circle, draw in OB and OC (which I did in the picture for you).

    [PLAIN]http://img249.imageshack.us/img249/4413/proof1f.jpg [Broken]
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Oct 15, 2011 #2


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    you might look in euclid where this is a standard theorem, probably in book III.

    by the way you have probably started it more or less correctly, as the first step in a circle proof is always to draw an appropriate line to the center.

    in fact the proof is immediate from your figure if you know the angle sum formula for a triangle, and the fact that a tangent is perpendicular to the radius.
  4. Oct 21, 2011 #3
    Consider drawing a line segment from the center of the circle, through the midpoint of BC, until it intersects AB.
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