Given any quadrilateral ABCD. Let X be the midpoint of side AB and Y be the midpoint of side CD. How can I prove that XY is not greater than max{AC, BD} ? Intuitively I see it is true in all cases, but don't have a clue how to prove this.
I started using the argument that XY <= AD, considering AD be the longest diagonal. This gives me two triangles ACD and ADB. Not sure whether that will help eventually or not. –