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Let a planar quadrangle $ABCD$ satisfy $AB = BC$ and $CD = DA$. Compute a point $P$ such that $PA+PB+PC+PD$ is minimum, for each of following two cases.

  1. The inner angle of $B$ is greater than $\pi$ but less than $2\pi$.
  2. All the inner angles of $A$, $B$, $C$ and $D$ are less than $\pi$ but greater than $0$.
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    ...please?!? Forget manners and tell us what have you done so far, ideas, insights, self effort...2012-11-25

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