Chapter 35 King's Cross Pg. 605
“And then . . . you know what happened. Reality returned in the form of my rough, unlettered, and infinitely more admirable brother. I did not want to hear the truths he shouted at me. I did not want to hear that I could not set forth to seek Hallows with a fragile and unstable sister in tow. “The argument became a fight. Grindelwald lost control. That which I had always sensed in him, though I had pretended not to, now sprang into terrible being. And Ariana . . . after all my mother’s care and caution . . . lay dead upon the floor.”
The "Ariana lay dead upon the floor" really stands out because if it was the Killing Curse that was used, then it explains why Dumbledore felt so much guilt. Not only did Grindelwald escape and make his dreams of dominating the muggle world and breaking the International Statute of Secrecy a reality, but he was also powerless against stopping Ariana from dying.
This might also be the reason why Dumbledore postponed his duel with Grindelwald until the very end, because if Grindelwald knew and revealed who had really killed Ariana, he might have stated that Dumbledore killed Ariana to scare Dumbledore and scar him emotionally for the rest of his life. This might have caused Dumbledore the duel between him and Grindelwald.
