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Math Help - circles and triangles problem

  1. #1
    Junior Member
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    circles and triangles problem

    Hi, everybody, i would like to use your help with thease two problems:

    1. there is a regular triangle ABC drawn in the circle. one point D is chosen on the arch AB. prove that AD+DB=DC.

    2. there is a triangle ABC and BD is a median. point T is on the BC.  \frac{BT}{TC} = \frac{3}{1}<br />
    BD and AT crosses in point M. calculate \frac{AM}{MT}=?
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  2. #2
    Member Traveller's Avatar
    Joined
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    1. By Ptolemy's theorem( Ptolemy's theorem - Wikipedia, the free encyclopedia ), we have: AB.CD = AD.BC + BD.AC.

    Since the triangle is equilateral, AB = BC = AC. So these cancel out in the above equation to give us the result.
    Last edited by Traveller; September 25th 2010 at 12:07 PM.
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