# 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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