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[harry potter] why didn't voldemort hide one of his horcruxes with fidelius charm?

before they said that voldemort did not trust anyone, he had genuine confidence in the bellatrix, enough to hand him the cup. he could have made her the secret keeper of the cave, for example.

another thing, he didn't need to say that this was a horcrux, he just had to say that it was an extremely valuable thing for him.
gpt
Voldemort was really confident No one would even know he had a horcrux, let alone more than one. Like it's mentioned in the books the items he used and the places he chose to hide them were just trophies and spots he wanted to establish permanent attachments to, the security was mostly to stop anyone stupid enough to accidentally get close to them.

With Bellatrix for example, like Harry says he left it with her not because he trusted her but because he had some reverence for the old vaults owned by old discarding family in gringotts, he gave her the cup just to establish a personal link with an ancient Gringotts vault owned by a noteworthy pureblood family.

The only reason Dumbledore figured out he had any horcruxes at all was because Lucius fucked up and tried to use one to screw over Dumbledore and Mr Weasley, even after Voldemort realised Dumbledore new about the book he didn't expect Dumbledore to question why he left a piece of soul so casually with a follower and start the whole investigation into Voldemorts big secret.