That is completely correct. You could also have left out the word 'at.'

Hi Misaru! You're nearly right: "I arrived home and found the thief had broken in. " A native speaker would say "I arrived home," not "at home". For some reason, the word "home" almost never goes with a preposition (except for when we say, "I'm at home"). For example, you say, "I'm going home," never "I'm going to home." Anyway, I hope you went well on your test :) Happy studying! Matt

Just a comment rather answer which had been given. A shorter form would be, "I arrived home to find a thief had broken in."

Valery is right. Without any prior context, you would say "a thief".

Why we use the? We don't know thief as person exactly. It's correct?