For an even set of points in the plane, choose a max-sum matching, that is, a perfect matching maximizing the sum of Euclidean distances of its edges. For each edge of the max-sum matching, consider the ellipse with foci at the edge's endpoints and eccentricity $2/\sqrt 3$. Using an optimization approach, we prove that the convex sets bounded by these ellipses intersect, answering a Tverberg-type question of Andy Fingerhut from 1995.

翻译：对于平面的一组偶数点, 请选择一个最大和最匹配的匹配点, 也就是说, 最匹配的极匹配点是其边缘的欧几里德距离的总和。 对于最大和对齐的每一个边缘, 都要考虑到边缘端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端端口端口端口端口端口端口端口端口端口端口端端口端端口端端口端端口端端口端口口口口口口口端口口口口口口口端端端端端口口口口口口口口口端端端口口口口端口口口端端口端口端口端口端口口口口口口口口口口口口口口口口口口口口口有1995 。