[alogo] Pirate's treasure

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The story: There is an island. Captain Hook visited it and buried his treasure there. To locate the place, he noticed: From the unique tree A in the island, looking north, on the left there is a house B. On the right there is a castle C. Walk from A to B and then orthogonally at equal distance to B*. Repeat with the castle. From A to C and then orthogonally at equal distance to C*. Join B*C* and locate the middle M. There is the treasure.
After he leaves the island, some clever guy cuts the tree. Returning to the island, after some years, he was able, though, to locate the treasure. This because M does not change, when the place A of the tree changes.
To see it consider two isosceli right-angled triangles {B'BM, C'CM} with a vertex at M. B'B*C'C* is a parallelogram for any position of point A. Its diagonals bisect on their middles etc....

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