Assume I would have four goats, two male and two female, fenced in a circular 154 mÂ² area around a graceful tiny cherry tree with circumference of 44 cm. Neither the two female goats nor the two male goats can graze in harmony with each other, thatâ€™s why I tie each of them with a line of length L (the same length for each goat) at the fence. How long can the respective line L of a goat be in order to ensure that the goat cannot reach the graceful tree, but has a maximum area to graze on?

(The head and neck together of each goat is 25 cm long

)