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How to discard negative solutions

from a geometric problem I obtain with $Assumptions = {a > 0, b > 0, c > 0} 
using Solve a series of solutions such as
  {b -> a, c -> a} but also {c -> -a - b}.
The latter one should obviously be discarded because it will be negative 
according to the assumptions (a>0, b>0) above.
How can these negative solutions being excluded by Mathematica V8 ? Positve[] 
and NonNegative[] do not help because quantities which are not NumericQ remain 
unevaluated. Help is appreciated.

Robert Kragler

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