**Re-opened**

I don't think it is obvious how to find the shortest chord that bisects
the area of a convex polygon. That is the question posed in this now closed post: [Shortest bisecting line](https://mathoverflow.net/q/312824/6094).
Perhaps one would have to use the algorithm below, modified to spin the direction
through $180^\circ$.

> Shermer, Thomas C. "A linear algorithm for bisecting a polygon." *Information Processing Letters* 41, no. 3 (1992): 135-140.