A "dilemme cornélien" is, nowadays, an expression commonly used in french to describe a situation where a impossible choice has to be made. This choice is between two options that both are as important to the subject as the other.
This expression was born from the french play writter: Pierre Coneille. He was a famous writter from the 17th century. His style were tragic comedies that often confronted the main protagonist to an impossible dilemma; usually between love and honour. His unique style can be seen, for example, in Le Cid were the hero has to choose between love and avenging his father.