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Math Help - Obvious problem with quadrilateral

  1. #1
    Senior Member Paze's Avatar
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    Obvious problem with quadrilateral

    I have a quadrilateral ABCD.

    A circle is inscribed ABCD with the diameter 8.

    AB = 12
    CD = 8

    AB is parallel to CD

    BC < AD

    Now looking at the picture here, it should be obvious that BC cannot be smaller than AD seeing as DK should always equal CP.

    Obvious problem with quadrilateral-probleminscribed.png

    What am I misunderstanding here?
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  2. #2
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    Re: Obvious problem with quadrilateral

    Quote Originally Posted by Paze View Post
    I have a quadrilateral ABCD.

    A circle is inscribed ABCD with the diameter 8.

    AB = 12
    CD = 8

    AB is parallel to CD

    BC < AD

    Now looking at the picture here, it should be obvious that BC cannot be smaller than AD seeing as DK should always equal CP.

    Click image for larger version. 

Name:	probleminscribed.png 
Views:	6 
Size:	4.2 KB 
ID:	29561

    What am I misunderstanding here?
    Revise your figure to show that the center of the circle must be on the bisectors of the angles.
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  3. #3
    Senior Member Paze's Avatar
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    Re: Obvious problem with quadrilateral

    Quote Originally Posted by votan View Post
    Revise your figure to show that the center of the circle must be on the bisectors of the angles.
    It seems mathematically incorrect to assume that if CD is 8 and the diameter is 8...Then the sides CP and DK ara not parallel...They should by all means be parallel, right?
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  4. #4
    Senior Member Paze's Avatar
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    Re: Obvious problem with quadrilateral

    I get it now. I'm misunderstanding that the tangent points do not necessarily mean the end points of my diameter.
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