# Circle containing circles

Level pending

The radius of the smallest circle circumscribing the following three circles -
$$x^2+y^2-4y-5=0$$
$$x^2+y^2+12x+4y+31=0$$
$$x^2+y^2+6x+12y+36=0$$
can be written as $$3+\frac{5}{36}\sqrt{a}$$.
What is the value of $$a+44$$?

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