回复：回复：有一题大家可以试试

2nd thought: (THIS IS NOT A BEST SOLUTION BUT HELP U FIND THE FINAL SOLUTION READ MY WHOLE POST PLS)

I used excel to calc the min distance:
1- go straightforward to a distance D (where D>10)
2- go circling to the starting point to less than a cycle, and you are insured to find the line in LESS than 360 degree cycle.
and this solution is better than D=10

degree

0 72.831852
15 70.81973078
29 70.00006448
30 69.98038823
32 69.95680653
34 69.95440755
36 69.97340921
38 70.01406705
45 70.33154021
60 72.0069
90 80.7853

the best solution is when D= 10.46 and the total distance is 69.9..... wait!
still we can optimize it via the methods below.....




3rd though. instead of going 'cycling' after reached the point that D units away from the center (note D>10). we only need to go though several straintlines instead of cycling.

then, OK. we just need to check follwing several conditions... the prefect triangler- square - 5, 6, 7,8 DuoBianXing (sorry, i am not math major).

i will leave it to you for the final solution... BUT this is still not a final answer! please see my next post