1. an apple of discord

　　any subject of disagreement and contention, the root of the trouble, dispute不和之因；祸根

　　eg: he throwing us an apple of discord, we soon quarreled again.

　　The dispute about inheriting estate formed an apple of discord between them

　　This problem seem to be an apple of discord between the Soviet Union and the USA.

　　2. The heel of Achilles/the Achilles’heel

　　a week point in sth that is otherwise without fault; the weakest spot

　　eg:

　　The shortage of fortitude is his heel of Achilles.

　　His Achilles’heel was his pride—he would get very angry if anyone criticized his work.

　　English might be his Achilles’heel.

　　3.Helen of Troy:

　　a beauty who ruins her country. A terrible disaster brought by somebody or sth you like best.

　　eg: It is unfair that historians always attribute the fall of kingdoms to Helen of Troy.

　　She didn’t think of the beautiful umbrella bought the day before should become a Helen of Troy in her family. Because of this she and her husband quarreled for a long time.

　　4.The Trojan horse:

　　the hidden danger; the covert wreckers; to engage in underhand activities

　　The superpowers are always sending the Trojan Horses to many countries in the world.

　　They are defeated only because of the Trojan horse to many countries in the world.

　　They are defeated only because of the Trojan horse in their country.