Level pending

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 $$L_{13}$$

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