Given two unit-diameter disks tangent to a given line and to each other, determining a region bounded by two circular arcs and a line segment, is the Ford disk packing of that region the unique packing that covers as much total area as possible, among all ways of packing the region with disks tangent to the line?

As usual, disks in a packing must have disjoint interiors. For background on Ford disk packings, see http://en.wikipedia.org/wiki/Ford_circle . Note that I am not asking about Apollonian packings; in my packings, all disks must be tangent to the bounding line segment.

I would also be interested in links to existing literature on other packing problems of a similar nature, where the, um, tiles in the packing (is there a more apt generic word than "tiles"?) are required to be tangent to one of the sides of the region being packed.