trilemma

[trahy-lem-uh]
noun
1.
a situation, analogous to a dilemma, in which there are three almost equally undesirable alternatives: His trilemma consisted in not knowing whether to acknowledge receipt, deny it, or simply leave.
2.
Logic. a form of argument in which three choices are presented, each of which is indicated to have consequences that may be unfavorable.

Origin:
1665–75; tri- + (di)lemma

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World English Dictionary
trilemma (traɪˈlɛmə)
 
n
1.  a quandary posed by three alternative courses of action
2.  an argument one of the premises of which is the disjunction of three statements from each of which the same conclusion is derived
 
[C17: formed on the model of dilemma, from tri- + Greek lēmma assumption]

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Example sentences
Health is an area where the trilemma clearly applies.
In order to think this through one has to return to the trilemma.
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