no

your answer is no better than this early one -
"此時，鴨子距岸3r/4。然後，鴨子沿直徑向岸遊3r/4=0.75r，同時狐狸須跑半個半徑為r的圓弧，即3.14r，抓鴨子。3.14r/0.75r > 4.鴨子先到岸而起飛。 "...

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 經典追逐，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.