# Radical Triangles!

There are three circles \(C_1,C_2,C_3\) given by the following respective equations:-

\[(x+4)^2+y^2=4\] \[x^2+(y-8)^2=1\] \[(x-1)^2+(y-1)^2=1\]

Let \(L_{ij}\) be defined as the locus of a point \(P\) such that tangents from \(P\) on \(C_i\) and \(C_j\) have equal lengths.

Find the area of the triangle formed by \(L_{12}, L_{23}\) and \(L_{13}\)