>> >>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