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Thread: Minimum of a quadrilateral

  1. March 9th 2009, 07:02 AM #1
    bigb
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    Minimum of a quadrilateral

    Let A, B, C, and D be the vertices of a convex quadrilateral. Convexity means that for each of the lines the quadrilateral lies in one of its half planes. Find the point P for which the minimum Min(d(P,A) + d(P,B) + d(P,C) + d(P,D)) is realized.
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  2. March 9th 2009, 07:37 AM #2
    red_dog
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    PA+PC\geq AC

    PB+PD\geq BD

    Then, PA+PB+PC+PD\geq AC+BD

    \min(PA+PB+PC+PD)=AC+BD\Rightarrow P=AC\cap BD
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