I mean vf is larger than that, the duck still can free

The question expects to see that when even V (fox) or V (cat) is at 4.60338811 times of V (duck), the duck can still free...

Cat or Fox at this speed (4.60338811 times of duck which is > 4.1415926 times), your answer is not related at all.

You have already figured out the right path before, maybe i jinjing-ed you...

answer is 鴨在半徑為x 的圓上與狐周旋於同一直徑遠端，然後沿切線遊完。 I belive you understand now.

Now i hope jinjing can understand as well - hehe