dilemma

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dilemma

 [dĭ-lem´ah]
any difficult or perplexing situation or problem; in bioethics, a situation requiring a choice between equally undesirable alternatives.

di·lem·ma

(di-lem'ă),
Predicament caused by conflicting, difficult, or otherwise unsatisfactory choices.
[G. conflict of choices, fr. di-, two, dual + lēmma, proposition]