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A similar definition applies to space curves and curves in n-dimensional Euclidean space. The point where the tangent line and the curve meet or intersect is called the point of tangency. The tangent line is said to be "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point.
The same reciprocal relation exists between a point P outside the circle and the secant line joining its two points of tangency. If a point P is exterior to a circle with center O, and if the tangent lines from P touch the circle at points T and S, then ∠TPS and ∠TOS are supplementary (sum to 180°). If a chord TM is drawn from the tangency ...
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 inclination, sometimes called inversive distance, is when the circles are tangent and oriented the same way at their point of tangency, when the two circles are tangent and oriented oppositely at the point of tangency, for orthogonal circles, outside the interval [,] for non-intersecting circles, and in the limit as one circle degenerates ...
A tangential quadrilateral (in blue) and its contact quadrilateral (in green) joining the four contact points between the incircle and the sides. Also shown are the tangency chords joining opposite contact points (in red) and the tangent lengths on the sides. The incircle is tangent to each side at one point of contact.
In geometry, an envelope of a planar family of curves is a curve that is tangent to each member of the family at some point, and these points of tangency together form the whole envelope. Classically, a point on the envelope can be thought of as the intersection of two "infinitesimally adjacent" curves, meaning the limit of intersections of ...
The point of osculation is also called the double cusp. Contact is a geometric notion; it can be defined algebraically as a valuation. One speaks also of curves and geometric objects having k-th order contact at a point: this is also called osculation (i.e. kissing), generalising the property of being tangent. (Here the derivatives are ...
Monge's theorem states that the three such points given by the three pairs of circles always lie in a straight line. In the case of two of the circles being of equal size, the two external tangent lines are parallel. In this case Monge's theorem asserts that the other two intersection points must lie on a line parallel to those two external ...