1. ## 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.

2. $PA+PC\geq AC$

$PB+PD\geq BD$

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

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