dilemma vs extremity

dilemma

noun
  • A difficult circumstance or problem. 

  • A type of syllogism of the form "if A is true then B is true; if C is true then D is true; either A or C is true; therefore either B or D is true". 

  • A circumstance in which a choice must be made between two or more alternatives that seem equally undesirable. 

  • Offering to an opponent a choice between two (equally unfavorable) alternatives. 

extremity

noun
  • A hand or foot. 

  • The most extreme or furthest point of something. 

  • A limb (“major appendage of a human or animal such as an arm, leg, or wing”). 

  • An extreme measure. 

How often have the words dilemma and extremity occurred in a corpus of books? (source: Google Ngram Viewer )