有一个思路，不知对错

In a vertical axis system, the center O is (0,0):

let cat at the bottom (3/2PI), cat run contra-clock-wise

Plan:
1) rat runs all the way vertical to cat's running direction until made a turn of angle of PI/2.
2) Then rat run toward the side along a straight line.

rat speed=v
when both rat and cat made an angle or PI/2, rat (at PI)is (积分(v*cos(0.2t)dt))from center. It's 5v, and in opposite to cat (at 0).

let rat run toward a point (P) at 3rd quarter (let line OP is angle A for horizontal axis). With 余弦定理, we have an equation of v and A.

v=10*(Squre root((PI+A)^2+cosA-1)/((PI+A)^2-1)

I know when A=0, we will have V=10/(PI+1). The minimum can be less, but I didn't know how to find it.