Question 1182659
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This problem was solved several years ago in the lesson


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/The-point-which-minimizes-the-sum-of-distances-to-vertices-of-a-given-quadrilateral.lesson>The point which minimizes the sum of distances to vertices of a given quadrilateral</A>


in this site.


So you can read the solution from that lesson.