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Math Help - Yes.. another circle theorem

  1. #1
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    Yes.. another circle theorem

    Hi I am currently stuck on this question
    If anybody could tell me how to approach this or offer any help then please post. Here is the question:




    Thanks for any help!

    If you need any more clarificaiton then please just ask

    SORRY! the point P is the intersection of the chord AC with chord BD
    Last edited by Geometor; December 22nd 2007 at 08:47 AM.
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  2. #2
    Senior Member JaneBennet's Avatar
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    You got B and C the wrong way round.



    Anyway, the problem is the same as saying that 3∠BOD = ∠COA.

    ∆POD is isosceles, so ∠POD = ∠PDO.

    ∴ ∠OPC = ∠POD + ∠PDO = 2∠POD

    ∆COD is isosceles, so ∠OCD = ∠ODC = ∠POD.

    ∴ ∠COA = ∠OPC + ∠OCD = 2∠POD + ∠POD = 3∠POD.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by JaneBennet View Post
    You got B and C the wrong way round.
    Well, if I had noticed that I wouldn't have spent an idle 20 minutes trying to do it! Good spot.

    -Dan
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  4. #4
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    Thanks Jane!
    but why does the labelling of a point matter so much? :S
    its just a label
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  5. #5
    Lord of certain Rings
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    Quote Originally Posted by Geometor View Post
    Thanks Jane!
    but why does the labelling of a point matter so much? :S
    its just a label

    Because the condition 3 BD = AC will be different for your figure
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