Statement
The sum of the distances between any point and the vertices inside a quadrilateral is less, then the perimeter of the quadrilateral.
Is the statement below always true for any quadrilateral?
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1 solution
For a simple counter-example, consider a kite-shaped quadrilateral and take the point to be very close to the vertex joining the larger two sides. We can make the other two sides of the quadrilateral small and the diagonal large to arrive at a contradiction.