[Closed] equidistant point

just wondering, does there exist a point (x,y) such that, it is equidistant to all the points in a given set
say for example i have a set of marbles placed at random points on the floor, now i want to add the next marble to this set of marbles such that it is equal distance from each of the marbles on the floor. using the distance formula i am getting:
d^2 = (x-x1)^2 +(y-y1)^2
d^2 = (x-x2)^2 +(y-y2)^2
d^2 = (x-x3)^2 +(y-y3)^2
d^2 = (x-x4)^2 +(y-y4)^2
d^2 = (x-x5)^2 +(y-y5)^2
…

is it possible to solve such a system of equations with 3 unknowns (x , y are the coordinates of the point which is at a distance of ‘d’ from all the other points ), if so how?

thanks!
any help is appreciated