  Huemer et al. (Discrete Math, 2019) proved that for any two finite point sets
$R$ and $B$ in the plane with $|R| = |B|$, the perfect matching that matches
points of $R$ with points of $B$, and maximizes the total squared Euclidean
distance of the matched pairs, has the property that all the disks induced by
the matching have a nonempty common intersection. A pair of matched points
induces the disk that has the segment connecting the points as diameter. In
this note, we characterize these maximum-sum matchings for any continuous
(semi)metric, focusing on both the Euclidean distance and squared Euclidean
distance. Using this characterization, we give a different but simpler proof
for the common intersection property proved by Huemer et al..
