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Tangent lines to circles. 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.
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 ...
Tangent circles. 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 ...
The nine-point circle is tangent to the incircle and excircles. In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant concyclic points defined from the triangle. These nine points are: [30] [31] The midpoint of each side of the triangle; The foot ...
Next to the intersecting chords theorem and the tangent-secant theorem, the intersecting secants theorem represents one of the three basic cases of a more general theorem about two intersecting lines and a circle - the power of point theorem.
Orthoptic (geometry) In the geometry of curves, an orthoptic is the set of points for which two tangents of a given curve meet at a right angle. Parabola. Orthoptic of the parabola (its directrix) Ellipse. Orthoptic of the ellipse (its director circle) Minimum bounding box of the ellipse ( circumscribed by the orthoptic circle) Major and minor ...
The points of intersection of two circles p and q orthogonal to a circle k, are inverses with respect to k. If M and M' are inverse points with respect to a circle k on two curves m and m', also inverses with respect to k , then the tangents to m and m' at the points M and M' are either perpendicular to the straight line MM' or form with this ...
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.