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If one circle is completely inside the other (< | |) then they have no bitangents, as a tangent line to the outer circle does not intersect the inner circle, or conversely a tangent line to the inner circle is a secant line to the outer circle. Finally, if the two circles are identical, any tangent to the circle is a common tangent and hence ...
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 ...
Ford circles also appear in the Sangaku (geometrical puzzles) of Japanese mathematics. A typical problem, which is presented on an 1824 tablet in the Gunma Prefecture, covers the relationship of three touching circles with a common tangent. Given the size of the two outer large circles, what is the size of the small circle between them?
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 ...
An Apollonian gasket with integer curvatures, generated by four mutually tangent circles with curvatures −10 (the outer circle), 18, 23, and 27. When four tangent circles described by equation (2) all have integer curvatures, the alternative fourth circle described by the second solution to the equation must also have an integer curvature ...
Let the radii of these two circles be denoted as r U, r V, respectively, and let their respective centers be the points U, V. 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).
A sex offender who police said tried to "financially and emotionally manipulate" his victims has been jailed for 25 years. Stephen Gallagher, of Normandy Avenue in Colchester, was found guilty by ...
All tangent circles to the given circles can be found by varying line . Positions of the centers Circles tangent to two circles. If is the center and the radius of the circle, that is tangent to the given circles at the points ,, then: