Mathematic solution

Hi all,

i somehow made my solution to be overcomplicated :/

i first calculated two lines defined by the first and second and by the second and third point, then, i found a normal to those lines going throught the middle points between the first and second and between the second and third point. After that, i calculated the intersection point of these two lines. My solution works, but is very long and not elegant. Obviously, there is some other, very easy algebraic solution to this task, allmost everyone here used. Please, can you point mo to some interent page, where the mathematic solution, used by most of the solver is described? Thanks a lot in advance