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Download as PDF; Printable version; ... Pages in category "Theorems about circles" ... Tangent–secant theorem This page was ...
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.
Kissing circles. Given three mutually tangent circles (black), there are, in general, two possible answers (red) as to what radius a fourth tangent circle can have. In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this ...
The tangent-secant theorem can be proven using similar triangles (see graphic). Like the intersecting chords theorem and the intersecting secants theorem, the tangent-secant theorem represents one of the three basic cases of a more general theorem about two intersecting lines and a circle, namely, the power of point theorem.
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, 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 ...
The circle packing theorem was first proved by Paul Koebe. [17] William Thurston [1] rediscovered the circle packing theorem, and noted that it followed from the work of E. M. Andreev. Thurston also proposed a scheme for using the circle packing theorem to obtain a homeomorphism of a simply connected proper subset of the plane onto the interior ...
Mutually tangent circles. Given three mutually tangent circles (black), there are in general two other circles mutually tangent to them (red).The construction of the Apollonian gasket starts with three circles , , and (black in the figure), that are each tangent to the other two, but that do not have a single point of triple tangency.