umm another naive solution for this would be to go from the center to any arbitrary end, do not cross on to the lake just wait around 2-3 meters from the bank a

umm another naive solution for this would be to go from the center to any arbitrary end, do not cross on to the lake just wait around 2-3 meters from the bank and wait for the monster. Once the monster reaches the bank just in a straight line to the other side. This way you will have to cover 2r distance where as the monster will cover 3.14r (pi*r ) distance . You will be able to out run a monster around 1.57 times your speed. Sure it is not that good enough but if your calculus isn't that good (To be honest calculus is the last thing on your mind when a monster is chasing you) and the monster is slow then you will be able to out run him.