[![enter image description here](https://i.stack.imgur.com/D7ihq.jpg)](https://i.stack.imgur.com/D7ihq.jpg)

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> Let a rope be fixed at a point "A". The other end of the rope (point "B") is attached (tangentially) to a horizontal drum which is 2m higher than point "A". The drum stretches the rope.
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> A vertical pillar is located off the vertical plane defined by points A & B. The rope is redirected by the pillar - i.e. it goes from "A" to the pillar and then turns to point "B".
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> At which height along the pillar will the tensioned rope turn?
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My reflections are that the rope either follows a steady slope, or the height along the pillar is the projection of the slope defined by points A & B, or that the length of the rope should be minimum. However I cannot find any source regarding this matter, and I cannot reach a proof for my reflections.