# Common tangent

Geometry Level 4

\begin{align} P_1 &: y = x^2 - ( 6 + 2 \sqrt{5} ) x + ( 22 + 6 \sqrt{5} ) \\ P_2 &: y = -x^2 + ( 6 + 2 \sqrt{5} ) x - ( 6 + 6 \sqrt{5} ) \end{align}

If the equation of the common tangent of the two parabolas $$P_1$$ and $$P_2$$ above is given by $$L : ax+by+c=0$$, where $$a,b \ge 0$$ and $$|b|$$ and $$|c|$$ are coprime, find $$a+b+c$$.

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