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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 ...
In geometry, a set of Johnson circles comprises three circles of equal radius r sharing one common point of intersection H.In such a configuration the circles usually have a total of four intersections (points where at least two of them meet): the common point H that they all share, and for each of the three pairs of circles one more intersection point (referred here as their 2-wise intersection).
intersection of two polygons: window test. If one wants to determine the intersection points of two polygons, one can check the intersection of any pair of line segments of the polygons (see above). For polygons with many segments this method is rather time-consuming. In practice one accelerates the intersection algorithm by using window tests ...
Pappus chain – Ring of circles between two tangent circles; Polar circle (geometry) – Unique circle centered at a given triangle's orthocenter; Power center (geometry) – For 3 circles, the intersection of the radical axes of each pair; Salinon – Geometric shape; Semicircle – Geometric shape; Squircle – Shape between a square and a ...
Angle AOB is a central angle. A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians). [1]
D, the other point of intersection of the two circles, is the reflection of C across the line AB. If C = D (that is, there is a unique point of intersection of the two circles), then C is its own reflection and lies on the line AB (contrary to the assumption), and the two circles are internally tangential.
As any two great circles intersect, there are no parallel lines in elliptic geometry. In elliptic geometry, two lines perpendicular to a given line must intersect. In fact, all perpendiculars to a given line intersect at a single point called the absolute pole of that line.
If the two given circles are tangent at a point, the Steiner chain becomes an infinite Pappus chain, which is often discussed in the context of the arbelos (shoemaker's knife), a geometric figure made from three circles. There is no general name for a sequence of circles tangent to two given circles that intersect at two points.