Triangle translated

Geometry Level pending

The triangle formed by the points \[{\rm{A}}\left( { - {\rm{9}},{\rm{ 29}}} \right),{\rm{ B}}\left( {{\rm{1}}5,\,22} \right), {\rm{C}}\left( {{\rm{3}},{\rm{ 13}}} \right)\]is translated parallel to the y-axis so that the sides AC and BC touch the circles \({x^2} + {y^2} + 16x - 2y - 35 = 0\)and \({x^2} + {y^2} - 20x - 4y + 79 = 0\)respectively at \(A'\)and \(B'\). Find the perimeter of the quadrilateral formed by \(A'\), \(B'\)and the corresponding new positions of A and B.

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