A got AC using real numbers with EPS = 1e-8, so precision is not major matter here...

i think it is safe to rotate point 1 90 degrees 4 times and check if it is possible to align the rotated point 1 with point 2 to form an edge of the square. rotated point1 will also have integer coordinates.

Thanks, Neal Zane!
Your idea is fruitful indeed. I've already gave up to overcome test#24, where float calculations seem to be very sensitive to precesion. And tan/atan along with sqrt gave me error of 10^-8. Now totally integer solution is concise and fast!

Thanks for idea. Simple and beautiful. My previous AC solution was more difficult.

I have tried this way. When I used the formula 2*(y0*x1 - y1*x0)^2 ? R^2*((x1 - x0)^2 + (y1 - y0)^2) (with 3 x <- -y, y <- x) (with long long on right side) has received WA 3.
My previous right solution with use of floats has no more lines and operations. Therefore I believe that geometrical problems to solve in the habitual ways (via floats with epsilon) more preferably.
It is necessary to use a "wheel", instead of to invent something new when good average speed of the decision of a problem is necessary.

I was very surprised, when after WA1 and WA 2 my solution was accepted :)

Pay attention to the situation, when points becomes the same.

Thanks! Very useful hint!