I need a general formula that calculates the equidistant locus of three points $(P_x,P_y)$; in terms of the coordinates of the three points $(A_x, A_y), (B_x,B_y), (C_x,C_y)$.
Setting the distances equal yielded nothing for me. Calculating the intersection of the equidistant locus of two pairs of points depended on the x and y coordinates being different for each point, making it impractical to use.