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There is a circular field of radius r1. There is a cow on the field. How long (r2) does the rope connecting the cow and the edge of the field need to be so that the cow can eat the grass only on half of the surface (S1(green)) of the field. Rope is anchored at O2 and the center of the field is at O1. S1=S2
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God damn it OP why didn't your mother just fucking abort you
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>>9080616
you just can't solve it
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>>9080629
I can't be arsed to find the exact answer but the length of the tether creates another circle with a limit in size of twice of the first circle. But the travresable area is limited to the area of the first circle. Find the rate at which the two circles over lap with respect to the increase in length of the cord and give an answer that's pretty a proximate because fuck circular measurments. The cird will be a little longer than the radius of the first circle since the center of the 2nd will always lie on the perimeter of the other circle.
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It's not really a riddle, more of a geometry problem.
Anyway here's an outline for solving it. You separate the green area into the Purple and Red areas shown and find their areas.
Finding the purple area is easy. You find the angle A using the law of cosines since the length of all three sites are known (two are r1, the one opposite of A is r2). Then subtract the area of the triangle from the area of the sector (both easy formulas to look up). And multiply it by two (two equal sections).
To find the red area, you first need to find the length of the blue line (you use that to find the angle of the sector using the law of cosines like above and then take the whole area of the sector). To find this blue length you take advantage of the properties of kites. In particular the blue line is perpendicular to the line from O1 to O2 (it doesn't look like it because bad drawing, but it's a kite, so it is). Then you just use the various properties of triangles (for example, using the law of cosine again, then all the various right-triangle properties blah blah blah) to find the half-length of the blue line and the rest writes itself.
Set the sum of the two (three) areas to be equal to half the area of the circle with radius r1 then math it out. Or plug it into Wolfram Alpha. And you got your answer.
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