Graphing Prevents Overthinking

Geometry Level 1

There are four lines that are tangent to both circles
x2+y2=1 and (x6)2+y2=4. { x }^{ 2 }+{ y }^{ 2 }=1 \quad \text{ and } \quad ({ x }-6)^{ 2 }+{ y }^{ 2 }=4.

What is the sum of the slopes of these four lines?

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