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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 angle between a chord and the tangent at one of its endpoints is equal to one half the angle subtended at the centre of the circle, on the opposite side of the chord (tangent chord angle). If the angle subtended by the chord at the centre is 90 ° , then ℓ = r √2 , where ℓ is the length of the chord, and r is the radius of the circle.
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 .
The tangential angle φ for an arbitrary curve A in P. In geometry, the tangential angle of a curve in the Cartesian plane, at a specific point, is the angle between the tangent line to the curve at the given point and the x-axis. [1] (Some authors define the angle as the deviation from the direction of the curve at some fixed starting point.
Tangent to a curve. The red line is tangential to the curve at the point marked by a red dot. Tangent plane to a sphere. In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point.
In the case in which the original triangle has no angle greater than 120°, this point is also the Fermat point. The Apollonius point is the point of concurrence of three lines, each of which connects a point of tangency of the circle to which the triangle's excircles are internally tangent, to the opposite vertex of the triangle.
A circle with 1st-order contact (tangent) A circle with 2nd-order contact (osculating) A circle with 3rd-order contact at a vertex of a curve. For each point S(t) on a smooth plane curve S, there is exactly one osculating circle, whose radius is the reciprocal of κ(t), the curvature of S at t.
Common lines and line segments on a circle, including a secant. A straight line can intersect a circle at zero, one, or two points. A line with intersections at two points is called a secant line, at one point a tangent line and at no points an exterior line. A chord is the line segment that joins two distinct points of a circle. A chord is ...