Let's consider a convex hexagon where we know the midpoints of each side.
I'm currently trying to show that if we connect the midpoints of the opposite sides into lines that the three lines will all intersect at one common point. Now because this was in the area unit of my work, I figured that it would have to relate to area in some way or another. And so far, I've been able to find that if you take any one of those three lines that connect the midpoints on the opposite sides of a hexagon, it will divide the hexagon into two pentagons, and these pentagons have an equal area to each other. But I'm not sure how to relate this information back to the problem. If anyone can help out, that would be create.