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I have a problem with next data:

  1. I have a grass meadow with the shape of circle, and its radius is "r"
  2. I have a goat on a leash.
  3. I need to know length of a leash and how far pale, where leash is attached, have to be from a grass circle (center or edge).

In simple words I need to know radius of a circle that can cut another circle into half and how far centers of those circles needs to be away.

Illustration:

enter image description here

Multiple explanations are welcome. I need this so my goat can eat exactly half of a grass meadow :)

And, length of a goat or where leash is attached to a goat doesn't matter :) Pole needs to be outside the meadow same as in illustration.

Senad Meškin
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  • Nothing, I'm software developer and I need to calculate this through software app, and I don't know where to start. Programming it is not a problem but logic, formula that is ;) – Senad Meškin Feb 08 '15 at 19:47
  • I have updated question,look at the end. – Senad Meškin Feb 08 '15 at 19:58
  • The formula for the area grazed is well-known -- see http://math.stackexchange.com/q/340421/139123 -- but you may have to apply numerical methods to get the solution you want. – David K Feb 08 '15 at 21:02

1 Answers1

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The problem so far is underdetermined. Put the pole anywhere, and let out more and more rope for the leash. If you let out exactly enough leash the goat will be able to just barely munch one blade of grass. If you let out too much he will be able to eat the entire meadow. So at some length in between he will be able to eat exactly half the grass. So there's no unique solution of pole placement. You could even have it in the meadow.

Matthew Leingang
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  • Right. @Senad, you can find a solution if you, say, tether the goat the boundary fence of the round field. That is, the center of the second circle lies on the circumference of the first. – Simon S Feb 08 '15 at 19:52
  • Another question is if the pole is right on edge, but I need it outside and pole needs to be outside first circle :) – Senad Meškin Feb 08 '15 at 19:56