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Math Help - circle geometry

  1. #1
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    circle geometry

    im stuck with this. help?

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  2. #2
    MHF Contributor red_dog's Avatar
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    Let CD be the tangent line passing through T, and B, C are at the same side of AT. Then

    \widehat{BPT}=\widehat{CTP}

    \widehat{PTB}=\widehat{PTC}-\widehat{BTC}=\widehat{BPT}-\widehat{BAT}=\widehat{PTA}
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  3. #3
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    circle geometry

    originally posted by Purebladeknight

    Hi PBK,
    A little late but I hope this unstucks you.
    Problem requires a multi-step proof. Here are some hints;
    1.Draw a diameter of smaller circle from P thru the circles center
    2.Mark intersections of AT and BT with smaller circle K and L.Connect KL
    3In order to prove anglesPTA and PTB equal arcs KP and PL must be shown equal.
    4What conclusion can be made about arcs TL and TB? about KL?
    If you need more help reply.

    BJH
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  5. #5
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    circle geometry

    posted by Purebladeknight

    Greetings Mate,

    Your diagram is great.Add the tangent @T .Mark the right side of line W
    1 angle BTW =1/2 arc TB=1/2 arcTL.arc TB=TL
    2 now prove KL is parallel to AB by showing that the transversal AT has two equal corresp angles.You know that KL is perpendicular to OP
    3 Draw KO and LO They are equal and PO is the perpendicular bisector of KL
    4 Rest is easy

    bjh
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