  Source localization is widely used in many areas including GPS, but the
influence of possible noises is not so negligible. Many optimization methods
are attempted to alleviate different kinds of noises. Needless to say the
stability of the solution, even the number of global solutions are not fully
known. Only local convergence or stability for the optimization problem are
known in simple $L^1$\cite{Kwon} or $L^2$\cite{Kwon3} settings. In this paper,
we prove that the number of possible two dimensional source locations with
three measurements in $L^2$ setting, is at most $5$, which is the complement
and correction to the previous work \cite{Kwon3}. We also showed the sufficient
and necessary condition for the number of the solutions being 1,2,3,4,and 5,
where the measurement triangle is isosceles and the measurement distance for
the two isosceles triangle bases are the same.
