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Math Help - easy circle geometry.

  1. #1
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    Question easy circle geometry.

    ABCD is a cyclic quadrilateral.AB and DC when produced meet at P.again AD and BC when produced meet at R.The circumcircles of triangles BCP and CDR intersect at T. prove that P,T,R are collinear.
    i have a soloution,but i want to use the Menelaus theorem or some trignometry to prove it. Is it possible to do so???
    please HELP!
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  2. #2
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    I cannot think of the method using Menelaus Theorem , seemingly it is very difficult for us to apply it ...


     \angle RDT = \angle  RCT = \angle  BPT

     \angle  CDT = \angle  CRT =  \angle  BRT

    Therefore  \angle  ADC = \angle  RDT + \angle   CDT = \angle  BPT + \angle   BRT also  \angle  ADC = \angle   ABR so we have


     \angle  BPT + \angle   BRT =  \angle   ABR

    Therefore  P,T,R lie on a straight line .
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  3. #3
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    thanks.please posts problems of similar flavour!
    Last edited by earthboy; July 1st 2010 at 11:30 PM.
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