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An idiom has meaning different from the meaning of individual words;idiomatic expression "on the horns of a dilemma"=Having to decide between 2 things,people,etc.Or it means faced with 2 equally undesirable alternatives;equally unpleasant.
eg:-Alice didn't know whom to choose to get married,man 23 or 63, and found herself " on the horns of a dilemma."
(2)to face a dilemma=to be in a dilemma.
eg:-In a dilemma or to be in a dilemma are comparable of one thing with another in two very difficult choice between two predicaments.