Hi Elang,
I may have misunderstood the problem with an assumption error on my part

I thought the question was about orientation and how to rotate the items like magenta lines. so i made the video (nephew in school meant very young to me).

I didnt see massive math.

I have assumed that x√2 is a result of A2 to C?

The angle of x defined by a circle of radius x. Thats how i start with circle and orient.

If you have random angle of x, i don't think the problem solves.

If i have made an error in reading the initial post, i must drop off as it is much deeper than i am capable