EPS=1e-8 precision for =0 comparisons is ok. Output 10 digits after decimal point is ok (6 digits gave WA41).

The point to find is called Fermat point, check at mathworld.wolfram.com

Yea, Fermat point.... or simple ternary search :)

Outputting 6 decimal points works just fine.

There is no need for epsilon tweaking: it can be solved with fractions (Python 3) except one Decimal (getcontext().prec=10) needed for sqrt(3).