Originally posted by Project Monkey
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Being as people were bored and someone asked for a puzzle....
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Originally posted by ASB View PostSo, circle 1 in the field.
Given the mythical goat is tether at the inside edge then the length of the tether defines another circle.
However it is bounded by the first circle, so defines an arc.
So the question is
"What is radius of a circle which is centered on the edge of another circle where the overlapping arc is equal to half the entire area of the overlapped circle"
At least I think that is the question.
At this point I hand over Bob to code up the solution.My subconscious is annoying. It's got a mind of its own.Comment
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Originally posted by pjclarke View PostSo it is, and there is a formula for overlapping circles, that I CBA to look up but which involves a square root and at least one cosine. The intersecting arcs define an area consisting of two segments the triangular height of which can be derived from the radiuses.
At this point I hand over Bob to code up the solution.Comment
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Originally posted by Contreras View PostYes, that is the question. Or is it?
Tether needs to be > radius of the field otherwise clearly it would reach less than half the field area. It needs to be < √2 or clearly the goat would reach more than half the field. So somewhere between 1.0 and 1.4ish.
However the maths seems so impossibly difficult that it must be a trick question. Is the tether fixed to a single point? I'm not sure that was stated. Anyway, off to google now...
Root 2 looks like it might have been the right answer (it isn't).
The 4 relevant areas are 2 segments with a chord of length r2 (on circle1). An isoceles triangle with sides of r2 and an angle unknown. The final piece being a chord with length the base of the isoceles triangle (on circle2).
It will involve using a cosine and an arc sine.
Maybe I should have listened a bit more in my geometry and trig all those years ago when I was about 13.Comment
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Oh, inside edge! Didn't read it properly, thought it looked too easy.bloggoth
If everything isn't black and white, I say, 'Why the hell not?'
John Wayne (My guru, not to be confused with my beloved prophet Jeremy Clarkson)Comment
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Originally posted by ASB View Post
The 4 relevant areas are 2 segments with a chord of length r2 (on circle1). An isoceles triangle with sides of r2 and an angle unknown. The final piece being a chord with length the base of the isoceles triangle (on circle2).
I can't remember the formula for the area of a segment, but you can be pretty sure it involves pi and the radius, the radius of the garden is fixed, and the radius of the goat's arc of nibbling is what we are trying to find.
If only I still smoked I could draw it on the back of a fag packet (c:Comment
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