G'morning again David...

 DW> I have developed a strong suspicion that, if the circles
 DW> overlap sufficiently to reduce the total area from 60 to 36
 DW> cm^2, then the area covered by all three will always be *more
 DW> than* 3 cm^2. However, I have not yet been able to prove this
 DW> in the general case.

 DW> Any ideas about this?

Accepting the 20cm^2 circles must cover 36cms^2 only gets you....

Cover  Segment Cm^2  Total Cm^2

Thrice  1.1572999     1.1572999
Twice   7.2284667    21.6854002
Once    4.3857666    13.1572999
        Totalling... 36.0000000 

Setting the thrice to 3 cm^2 then has the total coverage rise....

Thrice  3             3.0
Twice   1.0237947     3.0713841
Once   14.952411     44.857233
        Totalling... 50.9286171

Neither of these optimums fit the specifications given.

I'd conclude that the problem is geometrically impossible...

:-)
 
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