Assume that we have three collinear points
$A(x_0,y_0),B(x_1,y_1)$ and $C(x_2,y_2)$.
They are on three different circles whose centres and radii are respectively
$\big((P_x, P_y), r_P\big)$, $\big((Q_x, Q_y), r_Q\big)$ and $\big((R_x, R_y), r_R\big)$
The euclidian pairwise distances between three points are known.
How do I calculate if there is a unique solution for $(x_i, y_i)$ pairs s.t. $i = 0,1,2$?