  We consider matchings with diametral disks between two sets of points R and
B. More precisely, for each pair of matched points p in R and q in B, we
consider the disk through p and q with the smallest diameter. We prove that for
any R and B such that |R|=|B|, there exists a perfect matching such that the
diametral disks of the matched point pairs have a common intersection. In fact,
our result is stronger, and shows that a maximum weight perfect matching has
this property.
