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Tangent Circle

Definition

Two circles with centers at (x_i, y_i) with radii r_i for i = 1, 2 are mutually tangent if (x_1 - x_2)^2 + (y_1 - y_2)^2 = (r_1 ± r_2)^2. If the center of the second circle is inside the first, then the - and + signs both correspond to internally tangent circles. If the center of the second circle is outside the first, then the - sign corresponds to externally tangent circles and the + sign to internally tangent circles.

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