I know it’s the same thing, RickyBlender, but your diagram might be more convincing if you rotated the points so P2 was on the circle’s vertical radius, thus visually matching TynkaTopi’s original set up.
@TynkaTopi: Ricky is correct. The methods given can find A circle containing those two points, but not THE circle containing those points. When you ask geometrical questions, precise language is very important. Your question:
How to get the center of the circle between two points of the circle ?
says to a mathmetician that there is a unique circle that fits the requirements, otherwise it would ask: “how to get a center of some circle” which means you want a circle going through the points, but don’t particularly care which one.
Your second bit of information
I know that one of the vertices (right one on picture) is center of circle horisontally.
may have led you to believe you had more information than just two points, and so a unique solution would be possible, but, in fact, since circles are symetrical, that statement can be true about ANY point on a circle – it just depends on your point of view. So you really don’t know any more than the location of two points on the circumference. It is a geometrical fact that there are an infinite number of circles with the same two points on their circumference. To find a unique circle, you need another point.