Cat and Mouse

$N$ cats and $N$ mice are situated in a 2-D plane. Mota Chuha wants to choose $K$ number of animals in such a way that the distance between any pair of chosen cat and chosen mouse is minimized. Distance between the same type of chosen animals doesn't matter. In other words, suppose Chota Chuha chooses cats $C_1, C_2, \ldots, C_m$ and mice $M_1, M_2, \ldots, M_n$, then maximum of $Distance(C_i,M_j)