no

your answer is no better than this early one -
"此时，鸭子距岸3r/4。然后，鸭子沿直径向岸游3r/4=0.75r，同时狐狸须跑半个半径为r的圆弧，即3.14r，抓鸭子。3.14r/0.75r > 4.鸭子先到岸而起飞。 "...

See optimal route and solution see 皆兄弟's answer 10-05-12 18:59:12 he is incorrec just because he though fox was not smart.

this is a old and 经典追逐，numbers in my question is duck's minimum velocity (0.21723363 to fox) - all other numbers (1/4 1/ PI+1...) is not right for obvious reasons.