Tippy table
This square table used to be perfectly stable, back when it had a foot at the end of each leg. Now three of them are missing and there's only one left at leg A.
The table measures 50 cm x 50 cm. The foot is flat and attached by a swivel so that the end of leg A is a constant 0.5 cm from the ground.
The table can now rock back and forth with the foot of A and leg C in constant contact with the floor.
If B is also in contact with the floor (as pictured), how far is D from the floor?
Note: consider the tips of the legs to be singular points at the corners of a square.
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1 solution
If A didn't have a foot, the ends of the four legs would be coplanar. Since B and C are both touching the floor, A and D are at the same height: E x a c t l y 0 . 5 c m