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Positions Of Two Circles In A Plane

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Each circle is in the exterior region of the other. The distance between the centers of the circles are greater than the sum of their radii.
Two circles intersect at two points. The triangle inequality is satisfied between the radii and distance between the centers.
Two circles are internally tangent. The distance between the centers is the absolute value of the difference of the radii. The centers and the point of tangency are collinear.
Two circles are externally tangent. The distance between the centers is equal to sum of the radii. The centers and the point of tangency are collinear.
Two circles are orthogonal i.e they cut each other at right angles.

You can investigate the applications by moving the empty squared points.

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