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An inversion in their tangent point with respect to a circle of appropriate radius transforms the two touching given circles into two parallel lines, and the third given circle into another circle. Thus, the solutions may be found by sliding a circle of constant radius between two parallel lines until it contacts the transformed third circle.
Consider two ellipsoids, each with a given shape and orientation, whose centers are on a line with given direction. We wish to determine the distance between centers when the ellipsoids are in point contact externally. This distance of closest approach is a function of the shapes of the ellipsoids and their orientation.
The inclination, sometimes called inversive distance, is when the circles are tangent and oriented the same way at their point of tangency, when the two circles are tangent and oriented oppositely at the point of tangency, for orthogonal circles, outside the interval [,] for non-intersecting circles, and in the limit as one circle degenerates ...
In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point. There are two types of tangency : internal and external. Many problems and constructions in geometry are related to tangent circles; such problems often have real-life applications such as trilateration and maximizing the ...
If the circles have two points in common, the radical axis is the common secant line of the circles. If point P is outside the circles, P has equal tangential distance to both the circles. If the radii are equal, the radical axis is the line segment bisector of M 1, M 2.
The two given circles α and β touch the n circles of the Steiner chain, but each circle C k of a Steiner chain touches only four circles: α, β, and its two neighbors, C k−1 and C k+1. By default, Steiner chains are assumed to be closed, i.e., the first and last circles are tangent to one another.
Due to the Pythagorean theorem the number () has the simple geometric meanings shown in the diagram: For a point outside the circle () is the squared tangential distance | | of point to the circle . Points with equal power, isolines of Π ( P ) {\displaystyle \Pi (P)} , are circles concentric to circle c {\displaystyle c} .
The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a disc. The circle has been known since before the beginning of recorded history.