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Tangent lines to circles information


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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Tangent lines to circles

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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...

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Tangent circles

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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...

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Tangent

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Perpendicular Subtangent Supporting line Tangent cone Tangential angle Tangential component Tangent lines to circles Tangent vector Multiplicity (mathematics)#Behavior...

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Incircle and excircles

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all polygons do; those that do are tangential polygons. See also tangent lines to circles. Suppose △ A B C {\displaystyle \triangle ABC} has an incircle...

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Ford circle

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case of mutually tangent circles; the base line can be thought of as a circle with infinite radius. Systems of mutually tangent circles were studied by...

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Problem of Apollonius

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Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1). Apollonius of Perga (c...

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Soddy circles of a triangle

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mutually tangent quadruples of circles. Any triangle has three externally tangent circles centered at its vertices. Two more circles, its Soddy circles, are...

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List of circle topics

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circle Schoch circles Spieker circle Tangent circles Taylor circle Twin circles Unit circle Van Lamoen circle Villarceau circles Woo circles Circle-derived...

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Inscribed angle

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and the tangent line at one of its intersection points equals half of the central angle subtended by the chord. See also Tangent lines to circles. The inscribed...

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Orthogonal circles

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In geometry, two circles are said to be orthogonal if their respective tangent lines at the points of intersection are perpendicular (meet at a right...

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Diameter

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displaying wikidata descriptions as a fallback Tangent lines to circles – Line which touches a circle at exactly one point The diameters of a screwthread...

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Apollonian gasket

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starting with a triple of circles, each tangent to the other two, and successively filling in more circles, each tangent to another three. It is named...

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Pappus chain

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ring of circles between two tangent circles investigated by Pappus of Alexandria in the 3rd century AD. The arbelos is defined by two circles, CU and...

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Seven circles theorem

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circles all tangent to a seventh circle and each tangent to its two neighbors, the three lines drawn between opposite pairs of the points of tangency on the...

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Circle

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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...

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Power of a point

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two circles. Moving the lower secant (see diagram) towards the upper one, the red circle becomes a circle, that is tangent to both given circles. The...

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Malfatti circles

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geometry, the Malfatti circles are three circles inside a given triangle such that each circle is tangent to the other two and to two sides of the triangle...

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Apollonian circles

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geometry, Apollonian circles are two families (pencils) of circles such that every circle in the first family intersects every circle in the second family...

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Brocard points

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edge AB. These three circles have a common point, the first Brocard point of △ABC. See also Tangent lines to circles. The three circles just constructed are...

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Homothetic center

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corresponding diameters, which are thus parallel; see tangent lines to two circles for details. If the circles fall on opposite sides of the line, it passes through...

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Perpendicular

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circle, except the two endpoints of the diameter. The major and minor axes of an ellipse are perpendicular to each other and to the tangent lines to the...

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Belt problem

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belts found in airport luggage belts and automated factory lines. Tangent lines to circles Trigonometry examples in real life Archived April 25, 2009...

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Antiparallel lines

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antiparallel with respect to lines AB and AC, then all sections of the cone parallel to either one of these circles will be circles. This is Book 1, Proposition...

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Spherical circle

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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...

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