>>112377101) Circle
2) Round edges rectangle lines with thiccness of 2
3) The eye shape is the intersected area of two circles, and the goat is tied to two stakes each at the center of one of these circles
4) Forms a geometric shape called a "stadium", look it up.
5)a) free sliding rope attached to a stretched one, opposite to a simple rope on a stake, both ropes limiting the goat
5)b) Given the same length for all ropes, 2 free sliding ropes attached to 2 perpendicular stretched ones
5)c) Given one stretched rope is equal or longer than the paralel free sliding rope, 2 free sliding ropes attached to 2 perpendicular stretched ones
6)a) Let the free sliding ropes be long enough to intersect at the same point the stretched ropes would meet, create an angle between stretched ropes, then set 3 free sliding ropes attached to 3 stretched ones
6)b) Same as above but with 6 free sliding ropes attached 6 stretched ones
7)a) Both goat and dog tied to the same stake while the dog's rope is shorter
7)b) The goat is tied to one stake and the dog is tied to one free sliding rope of same length L on a stretched rope as close as L between two points at least 2L far apart
7)c) 3 dogs on 3, L_1 L_2 L_3 long, free sliding ropes on 3 stretched ropes between 3 stakes, so that L_x is shorter than the orthocenter and its foot.
8)a) Yes, because a triangle with altitude smaller than its respective side's rope would fully beinside the semicircle of one goat's range
8)b) Yes, because a quadrilateral isn't necessarily a rectangle and the opposing semi-circles might not intersect, meaning that their areas aren't limited to be smaller than the quadrilateral.
