In Euripides' Medea, the title character discovers that her husband Jason is going to divorce her and marry the daughter of Creon, who is the king of Corinth. Initially, Creon decides that Medea should be exiled as soon as possible.
The reason for this is that Medea's reputation precedes her. She is skilled in the arts of dangerous magic. By the time Medea reaches Corinth, she already directly or indirectly brought about the deaths of several people, including her own brother, Absyrtus, and the king of Iolcus, Pelias.
Given Medea's past, plus the fact that Medea will be enraged because of Jason's abrupt and unjustified divorce of her, Medea is likely to be a very dangerous woman. Moreover, Creon has already heard that Medea has been making threats against his daughter:
"Many things lead me
to this conclusion: you're a clever woman,
very experienced in evil ways;
you're grieving the loss of your husband's bed;
and from reports I hear you're making threats
to take revenge on Jason, on his bride,
and on her father." (Ian Johnston translation)
Unfortunately for Creon, Medea persuades him to allow her to remain in Corinth one more day. That is all the time Medea needs to orchestrate the murder of Creon's daugther. Creon himself is also killed in this plot.