Trilaterate your position
Desmos, 122 bytes

Online use. Copy+paste each equation into an equation box, click "add all" for each box, then click on the point of intersection, then enter in each value as appropriate. each of A, B, and C are the distances for the points (a,b), (c,d), and (E,f), respectively. To get a square root in the value, type sqrt then the value in the box.

\left(x-a\right)^2+\left(y-b\right)^2=AA
\left(x-c\right)^2+\left(y-d\right)^2=BB
\left(x-E\right)^2+\left(y-f\right)^2=CC


Verify the first test case.

Or you can take a look here: