>>
>>A perfect goat is tethered by a perfect rope at the edge of a perfectly
>>circular field. The field is enclosed by a (perfect) fence such that
>>the goat can not stray outside the confines of the field. How long must
>>the rope be in order that the goat can eat exactly half the surface
>>area of the field?
>>
>
>I have seen a couple of responses to this and, unless I am reading it
>wrong, the responders are reading it wrong. According to the above,
>the goat is tethered to an edge of the field and not to a post in the
>middle of the field. Therefore the length of the rope must be somewhat
>greater than the diameter of the field in order for the goat to be able
>to cover half the surface.
>
>Could it be that if the circle were of radius R, then the rope's length
>would be the hypotenuse of a triangle whose sides are of length R and
>R/2 ???????
 
Hmmmm. I read it wrong also...
The field is a whole circle.
The 'eating portion' of the field actually consists of two areas bounded
by 2 arcs and sharing the same chord.
 
Elbert