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Two different methods may be used to construct the external and internal tangent lines. External tangents Construction of the outer tangent. A new circle C 3 of radius r 1 − r 2 is drawn centered on O 1. Using the method above, two lines are drawn from O 2 that are tangent to this new circle.
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 ...
For any two circles in a plane, an external tangent is a line that is tangent to both circles but does not pass between them. There are two such external tangent lines for any two circles. Each such pair has a unique intersection point in the extended Euclidean plane. Monge's theorem states that the three such points given by the three pairs of ...
The same holds true for a line and a circle. Two distinct lines cannot be tangent in the plane, although two parallel lines can be considered as tangent at a point at infinity in inversive geometry (see below). [5] [6] The solution circle may be either internally or externally tangent to each of the given circles.
Koebe–Andreev–Thurston theorem: If G is a finite maximal planar graph, then the circle packing whose tangency graph is isomorphic to G is unique, up to Möbius transformations and reflections in lines. Thurston observes that this uniqueness is a consequence of the Mostow rigidity theorem. To see this, let G be represented by a circle packing.
If the incircle is tangent to the sides AB, BC, CD, DA at T 1, T 2, T 3, T 4 respectively, and if N 1, N 2, N 3, N 4 are the isotomic conjugates of these points with respect to the corresponding sides (that is, AT 1 = BN 1 and so on), then the Nagel point of the tangential quadrilateral is defined as the intersection of the lines N 1 N 3 and N ...
The tangent lines must be equal in length for any point on the radical axis: | | = | |. If P, T 1, T 2 lie on a common tangent, then P is the midpoint of ¯.. In Euclidean geometry, the radical axis of two non-concentric circles is the set of points whose power with respect to the circles are equal.
Hexagonal paper shows regular hexagons instead of squares. These can be used to map geometric tiled or tesselated designs among other uses. Isometric graph paper or 3D graph paper is a triangular graph paper which uses a series of three guidelines forming a 60° grid of small triangles. The triangles are arranged in groups of six to make hexagons.