Let's say I got $3$ points: $(lat_1, lon_1), (lat_2, lon_2), (lat_3, lon_3)$ and their distances to the point $p$ I want to know are $d_1, d_2, d_3$.
I can also know the distance between the points using Haversine Formula. How can I calculate the latitude and longitude of the point $p$?
Finally found the solution (didn't know the gis.stackexchange site):
Just have to pass the latitude and longitude coordinates to the cartesian ECEF, an then resolve an equation system having 3 circles that had as center one of each points and the distance to the point as radius.
Basically what I was missing was passing to the cartesian ECEF.
Since this is very far from what I use to do, take it with care
This problem looks very much to me as a data reconciliation problem (or least-square fit) and, so, I suggest to use the most natural variables.
Name $x$ the latitude and and $y$ the longitude of the point $p$ you are looking for. Compute the distances $d_1^*,d_2^*,d_3^*$ from the assumed latitude and longitude of point $p$ to the known points (each of the $d_i^*$ is a function of $x$ and $y$).
Now, define an error function such as $$\Phi(x,y)=(d_1^*-d_1)^2+(d_2^*-d_2)^2+(d_3^*-d_3)^2$$ and the idea is to minimize it and, hopefully, to get $0$ if the measures are exact. If they are not, this will give the best approximation of the location of point $p$.
