Each of the cameramen wants Lev to skate along a segment of a straight line from some point to another (and each has specified his own pair of points). Lev has decided to skate along all the specified segments passing from a segment to a segment along a circular arc so that his trajectory has the shape of a smooth curve.

Do Lev move in a circular arc or a straight line?

If there is no arc connecting two consecutive directed segments without breaks, Lev can extend one of the segments so as to connect them by an arc.

For example 2, do these circles valid to this statement?
(-1,-1) radius = sqrt(26)
(1,1) radius = 3*sqrt(2)
(0,0) radius = 2*sqrt(5)

but (-2,-2) radius = 6 is invalid because the endpoint of the segment doesn't end in this circle.
Am I right?

And Finally how do you compute 7.1415926536?
because I find that circle (-1,-1) could yield better solution for about 6.69659557624

None of these circles are valid because you should construct a SMOOTH curve, containing ALL the segments described in the test (and also don't forget about their direction). The only valid circle is (0,0) radius = 4.  And Lev can't move on it faster than sqrt(4) = 2. That's why we have such answer.