Assume the circles are actually open disks, otherwise two circles each of area $\frac{1}{2}$ wouldn't fit into the circle of area 1.

This seems like it should be true, thinking about packing density, but I've not been able to find an algorithm that works in all cases.

Assume the circles are actually open disks, otherwise two circles each of area $\frac{1}{4}$ wouldn't fit into the circle of area 1.

This seems like it should be true, thinking about packing density, but I've not been able to find an algorithm that works in all cases.