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