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Math Help - Triangle inscribed in two circles...

  1. #1
    mdk
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    Triangle inscribed in two circles...

    I need help with the set up of this problem...

    Two circles meet at points P & Q. Let segment AP and segment BP be diameters of the circles. Show that segment AB passes through the other intersection Q. See attached file.

    Any help would be greatly appreciated...
    Attached Thumbnails Attached Thumbnails Triangle inscribed in two circles...-2-circles-meet-p-q.jpg  
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  2. #2
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    Can we say angle PQA = angle PQB = 90 degree thus PQ perp AQB and so AQB is a line?
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  3. #3
    mdk
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    Yes. That is what I thought later after working on it for a while. Thanks for the help.
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    Quote Originally Posted by pragraphic View Post
    Can we say angle PQA = angle PQB = 90 degree thus PQ perp AQB and so AQB is a line?
    Quote Originally Posted by mdk View Post
    Yes. That is what I thought later after working on it for a while. Thanks for the help.
    If you add the radii in the 2 circles you get 2 isosceles triangles with the common base PQ. For symmetry reasons PQ \perp CM.

    Since C respectively M bisect the diameters the triangles ABP is similar to triangle CMP. Thus you can show that AB is a straight line and that AB is twice as long as CM.
    Attached Thumbnails Attached Thumbnails Triangle inscribed in two circles...-zweikrs_mittelparallel.png  
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