We consider matchings between a set R of red points and a set B of blue points with diametral disks. In other words, for each pair of matched points p ¿ R and q ¿ B, we consider the diametral disk defined by p and q. 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. More precisely, we show that a maximum weight perfect matching has this property