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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.
A stronger form of the circle packing theorem asserts that any polyhedral graph and its dual graph can be represented by two circle packings, such that the two tangent circles representing a primal graph edge and the two tangent circles representing the dual of the same edge always have their tangencies at right angles to each other at the same ...
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 , are tangent from different sides of (one in and one out), is the length of the interior common tangent. The converse of Casey's theorem is also true. [4] That is, if equality holds, the circles are tangent to a common circle.
In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is completely inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear. For any two circles in a plane, an external tangent is a line that is tangent to both circles but ...
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. For this reason the radical axis is also called the power line or power bisector of the two circles. In detail:
The Pappus chain consists of the circles in the shaded grey region, which are externally tangent to C U (the inner circle) and internally tangent to C V (the outer circle). Let the radius, diameter and center point of the n th circle of the Pappus chain be denoted as r n , d n , P n , respectively.
English: Every circle which is tangent to two given circles touches them at a pair of anti-homologous points. Source: Own work: Author: ... Category:Geometry ...
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