In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs. Since the tangent line to a circle at a point P is perpendicular to the radius to that point, theorems involving tangent lines often involve radial lines and orthogonal circles.
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geometry, tangentcircles (also known as kissing circles) are circles in a common plane that intersect in a single point. There are two types of tangency: internal...
all polygons do; those that do are tangential polygons. See also tangentlinestocircles. Suppose △ A B C {\displaystyle \triangle ABC} has an incircle...
case of mutually tangentcircles; the base line can be thought of as a circle with infinite radius. Systems of mutually tangentcircles were studied by...
Euclidean plane geometry, Apollonius's problem is to construct circles that are tangentto three given circles in a plane (Figure 1). Apollonius of Perga (c...
mutually tangent quadruples of circles. Any triangle has three externally tangentcircles centered at its vertices. Two more circles, its Soddy circles, are...
circle Schoch circles Spieker circleTangentcircles Taylor circle Twin circles Unit circle Van Lamoen circle Villarceau circles Woo circlesCircle-derived...
and the tangent line at one of its intersection points equals half of the central angle subtended by the chord. See also Tangentlinestocircles. The inscribed...
In geometry, two circles are said to be orthogonal if their respective tangentlines at the points of intersection are perpendicular (meet at a right...
displaying wikidata descriptions as a fallback Tangentlinestocircles – Line which touches a circle at exactly one point The diameters of a screwthread...
starting with a triple of circles, each tangentto the other two, and successively filling in more circles, each tangentto another three. It is named...
ring of circles between two tangentcircles investigated by Pappus of Alexandria in the 3rd century AD. The arbelos is defined by two circles, CU and...
circles all tangentto a seventh circle and each tangentto its two neighbors, the three lines drawn between opposite pairs of the points of tangency on the...
generalised circles are actually circles: a generalised circle is either a (true) circle or a line. The tangent line through a point P on the circle is perpendicular...
two circles. Moving the lower secant (see diagram) towards the upper one, the red circle becomes a circle, that is tangentto both given circles. The...
geometry, the Malfatti circles are three circles inside a given triangle such that each circle is tangentto the other two and to two sides of the triangle...
geometry, Apollonian circles are two families (pencils) of circles such that every circle in the first family intersects every circle in the second family...
edge AB. These three circles have a common point, the first Brocard point of △ABC. See also Tangentlinestocircles. The three circles just constructed are...
corresponding diameters, which are thus parallel; see tangentlinesto two circles for details. If the circles fall on opposite sides of the line, it passes through...
circle, except the two endpoints of the diameter. The major and minor axes of an ellipse are perpendicular to each other and to the tangentlinesto the...
antiparallel with respect tolines AB and AC, then all sections of the cone parallel to either one of these circles will be circles. This is Book 1, Proposition...
analogous to planar circles are called small circles or lesser circles. If the sphere is embedded in three-dimensional Euclidean space, its circles are the...