How do you calculate the angle i should rotate the whole circle to place the next circle perfectly touching at a single intersect?
each circle is exactly the same size
I tried it with drawing another circle from the center but it intersects at 2 points.
If you draw a triangle from the center of the big circle to the centers of the two small ones, then it'll be isosceles, and trigonometry tells us that the angle at the top is 2*asin(r/R) where R is the radius of the large circle and r is the radius of the small one. I don't fully understand what you're asking but that should help.
Oh, ok, well that's not too hard with some trig. The angle between lines from the centers of two equal-sized circles with radius r that go to the center of the big circle with radius R is 2asin(r/(R-r))