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Math Help - Circle Geometry: Difficult Proving Parrallel Lines

  1. #1
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    Circle Geometry: Difficult Proving Parrallel Lines

    AB and AC are equal chords of a circle. AD and BE are parallel chords through A and B respectively. Prove that AE is parallel to CD.
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  2. #2
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    Note that if a cyclic quadrilateral is a trapzeium , then it is an isosceles trapzeium . If a pair of the opposite sides are equal in length , then it is also an isosceles trapzeium .


    To prove the first line , Let  ABCD is a cyclic quadrilateral , assume it is a trapzeium , say  AB \parallel CD , then we have  \angle ABD = \angle BDC so  \text{arc} AD = \text{arc} BC  \implies AD = BC thus it is an isos. trapzeium .

    I give the proof of the second line to you .


    By applying the above property , we find that  DE = AB = AC so  AE \parallel CD
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  3. #3
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    Sorry, I am not so sure ABCD is concyclic. As ABCE is the actual quad inside circle.

    EDIT: nvm, i have found solution anywaz.
    Last edited by Lukybear; July 12th 2010 at 01:16 AM.
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