Was Dumbledore in love with grendlewald?

Arianna, his sister.

A fight broke out after an argument between Grindelwald and Dumbledore during their youth. Grindelwald and Dumbledore had a duel and Dumbledore believes he might have killed his sister by accident.

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There is no evidence Dumbledore killed Ariana. It could have been any of the three of them; Albus, Aberforth or Grindelwald. Dumbledore tells Harry that his greatest fear was that he struck the blow that ended her life, but Harry chooses not to ask whether he ever found out who was responsible for killing her, so we don't know. In fact, there is nothing any where that says Dumbledore killed anyone and considering his disdain for murder and the value he placed on intact souls (which are ripped apart when one kills), it is not likely he ever did.