Circle and tangents

Geometry Level 4

The tangent at \((1,2)\) to the circle \(C_{1}: x^2+y^2=5\) intersects the circle \(C_{2}:x^2+y^2=9\) at \(A\) and \(B\); and the tangents at \(A\) and \(B\) on \(C_{2}\) meet at \(P\). If the coordinate of \(P\) is in the form \(\left(\dfrac{a}{b},\dfrac{c}{d}\right)\), where \(a,b\) are positive coprime integers, and \( c,d\) are positive coprime integers, then find \(a+b+c+d\).

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