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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 ...
An inversion in their tangent point with respect to a circle of appropriate radius transforms the two touching given circles into two parallel lines, and the third given circle into another circle. Thus, the solutions may be found by sliding a circle of constant radius between two parallel lines until it contacts the transformed third circle.
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.
All tangent circles to the given circles can be found by varying line . Positions of the centers Circles tangent to two circles. If is the center and the radius of the circle, that is tangent to the given circles at the points ,, then:
Book 3 of Euclid's Elements deals with the properties of circles. Euclid's definition of a circle is: A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre.
The locus of the centers of all the osculating circles (also called "centers of curvature") is the evolute of the curve. If the derivative of curvature κ'(t) is zero, then the osculating circle will have 3rd-order contact and the curve is said to have a vertex. The evolute will have a cusp at the center of the circle.
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More generally, in geometry, two curves are said to be tangent when they intersect at a given point and have the same direction at that point; see for instance tangent circles; Bitangent, a line that is tangent to two different curves, or tangent twice to the same curve; The tangent function, one of the six basic trigonometric functions