How did Dumbledore discover Voldemort's cave

Places - The cave by the sea

Contribution from Jocelyn1 »

Places - The cave by the sea
The cave by the sea is located directly on the British coast and so far only played a role in the Harry Potter series. At the end of the 6th volume there is a decisive action. Dumbledore and Harry suspect a Horcrux in this cave.
This place is already mentioned at the beginning of the 6th volume. Here Harry learns that Lord Voldemort had already had experiences with the cave in his childhood in the orphanage. During the orphanage's annual summer excursion to the sea, the young Tom Riddle and two other small children had illegally reached this cave, presumably to scare the two children; so it was once told to Dumbledore by the owner of the orphanage.
Through Dumbledore's stories we learn that the cave is extremely difficult to reach for Muggles. It is only accessible to the most experienced mountaineers. Boats cannot reach the cave due to a strong current. So it becomes clear that even then Tom Riddle only got there with magic.
In the 7th volume, the house elf Kreacher Harry tells how his master, Regulus Arcturus Black, who was Voldemort's supporter at the time, gave Kreacher to Voldemort to hide the Horcrux in that very cave. In the cave, Voldemort made Kreacher drink a poisonous potion from a stone basin, put the Horcrux in it, refilled the basin with the potion, and left the tortured house-elf alone in the cave. However, the elf returned to his master (magic of a house elf) and told him about it. He recognized the terrible deeds of the great wizard and set out to destroy the horcrux, a medallion. He died trying, but was still able to hand the Horcrux to Kreacher and place a similar, simple medallion in the stone basin.
The cave only plays a role again when Dumbledore finds out about the Horcrux. In order to track down the Horcrux suspected there, the Headmaster and Harry Apparate onto a nearby rock, which they climb down. From there they go into the water and swim towards a crevice in the rock face that opens into a narrow tunnel. The tunnel opens into a large vestibule. Access to the actual cave was blocked by Lord Voldemort with magic. Dumbledore finally splatters the rock face with blood and the two of them see a huge lake through the opening that has now appeared. The dimensions of the cave can only be described slightly: it is not possible to see the ceiling of the cave or the other end of the cave. However, there seems to be a greenish shining rock island in the middle of the lake. The two magicians walk on a narrow path around the lake along the rock face and finally reach the island with the help of an autonomous boat. On the island the two discover the stone basin and Dumbledore drinks the poisonous potion in agony. The now enormously weakened wizard asks for water and after Harry tries several times with the spell Aguamenti he wants to fill a cup with water from the lake. We learn that the lake is filled with inferi (= dead bodies that are commanded by Voldemort) for such purposes, so that Harry is almost killed. Enormously weakened, Dumbledore can leave the cave with Harry and the wrong locket.

I tried to take into account everything I found in the books that I thought was important. For example, I have. omit the small cutout in the 7th volume. It mentions how Voldemort found out about the stolen Horcrux.

Important !!: Unfortunately, my name is different here than in because the computer told me that the nickname was already taken!
At Magic Hogwarts, my name is Jocelyn and I come from Ravenclaw.

Kind regards, Jocelyn