The significant line is:
* "You plotted it all. You had him killed, and then you thought you could blind me too, so you wouldn't be found out." (Translation by Robert Fagles)
This accusation is the catalyst for Oedipus's own realization. It triggers a chain of events that lead him to uncover the truth about his parentage and the murder of Laius, culminating in his anagnorisis.
It's important to note that the anagnorisis is a gradual process, not a sudden revelation. The line above acts as a turning point, but it's the subsequent events and Oedipus's own questioning that lead him to the full recognition of his tragic fate.