"A színházban kergették a rendőrök a fiatal bűnözőt."

Translation: The police officers were chasing the young criminal in the theatre.

[SedatKlc]

so what's the difference between kerget and üldöz?

[vvsey]

I think "kerget" is more literal and more specific. And closer. You run, I run after you, you are in my sight, that is "kerget".
"Üldöz" is a synonym but it is not necessarily a physical race. It can mean "fight" or "be against" something. For example, "crime fighters" are "bűnüldözők".

[zalfbuffel]

It might be confusing that the official translations given here and for the sentence with "üldöz" (https://forum.duolingo.com/comment/21258644) use a different verb tense ("chased" vs. "were chasing"). I asked a native speaker, and according to him there is no such difference in meaning, only the difference indicated by vvsey. "Kerget" also sounds slightly more playful to him: "A kutya kergeti a farkát" vs. "Az Illuminati üldöz engem".

[Imre565437]

iluminátus