Manipulate[
Block[{deta1, deta2, p1, p2, q, a1, b1, a2, b2, outerLine1,
outerLine2, innerLine1, innerLine2},
{{a1, b1}, {a2, b2}} = p;
deta1 = (a1 - a2)^2 + (b1 - b2)^2 - (r1 + r2)^2;
deta2 = (a1 - a2)^2 + (b1 - b2)^2 - (r1 - r2)^2;
p1 = r1 (a2^2 + b2^2 - a1 a2 - b1 b2);
p2 = r2 (a1^2 + b1^2 - a1 a2 - b1 b2);
q = a1 b2 - a2 b1;
innerLine1 = ((a2 - a1) (r1 + r2) + (b1 - b2) Sqrt[
deta1]) x + ((b2 - b1) (r1 + r2) + (a2 - a1) Sqrt[deta1]) y -
p1 + p2 + q Sqrt[deta1] == 0;
innerLine2 = ((a2 - a1) (r1 + r2) - (b1 - b2) Sqrt[
deta1]) x + ((b2 - b1) (r1 + r2) - (a2 - a1) Sqrt[deta1]) y -
p1 + p2 - q Sqrt[deta1] == 0;
outerLine1 = ((a2 - a1) (r1 - r2) + (b1 - b2) Sqrt[
deta2]) x + ((b2 - b1) (r1 - r2) + (a2 - a1) Sqrt[deta2]) y -
p1 - p2 + q Sqrt[deta2] == 0;
outerLine2 = ((a2 - a1) (r1 - r2) - (b1 - b2) Sqrt[
deta2]) x + ((b2 - b1) (r1 - r2) - (a2 - a1) Sqrt[deta2]) y -
p1 - p2 - q Sqrt[deta2] == 0;
Show[Graphics[{Circle[{a1, b1}, r1], Circle[{a2, b2}, r2]}, PlotRange -> 6, Frame -> 1],
ContourPlot[ Evaluate@{outerLine1, outerLine2, innerLine1, innerLine2}, {x, -5,5}, {y, -5, 5}]]
], {{p, {{-3, 1}, {3, 0}}}, Locator}, {{r1, 1}, 1, 3}, {{r2, 2}, 1,
3}]
