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A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter.
Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
The red curve is an epicycloid traced as the small circle (radius r = 1) rolls around the outside of the large circle (radius R = 3).. In geometry, an epicycloid (also called hypercycloid) [1] is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle.
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.
The radius of this Apollonius circle is + where is the incircle radius and is the semiperimeter of the triangle. [ 27 ] The following relations hold among the inradius r {\displaystyle r} , the circumradius R {\displaystyle R} , the semiperimeter s {\displaystyle s} , and the excircle radii r a {\displaystyle r_{a}} , r b {\displaystyle r_{b ...
It is the curve traced out by a point fixed to a circle (where the point may be on, inside, or outside the circle) as it rolls along a straight line. [1] If the point is on the circle, the trochoid is called common (also known as a cycloid ); if the point is inside the circle, the trochoid is curtate ; and if the point is outside the circle ...
The area of an annulus is the difference in the areas of the larger circle of radius R and the smaller one of radius r: = = = (+) (). As a corollary of the chord formula, the area bounded by the circumcircle and incircle of every unit convex regular polygon is π /4
The useful minimum bounding circle of three points is defined either by the circumcircle (where three points are on the minimum bounding circle) or by the two points of the longest side of the triangle (where the two points define a diameter of the circle). It is common to confuse the minimum bounding circle with the circumcircle.