Let $P$ be a set of points in the plane, and con­sider a per­fect, max­i­mum weight match­ing $M$ of $P$, where weight is de­fined by the sum of the Eu­clid­ean dis­tances be­tween matched points. For points $p$ and $q$, let the di­ame­tral disk $D_{pq}$ be the disk with $p$ and $q$ on the bound­ary that is cen­tered at the mid­point of $pq$. Let $D_M$ be the set of di­ame­tral disks of $M$. We show that the disks of $D_M$ have a com­mon in­ter­sec­tion. This was shown to be true by Hue­mer et al. for max­i­mum weight match­ings of red and blue points, with weight de­fined as the sum of the Eu­clid­ean dis­tances squared. Our re­sult dif­fers in that we do not square the dis­tances, and we per­mit match­ing any pair of points.