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The radius of a circle

In geometry, the radius of a circle or sphere, written as [math]r[/math],[1] is the shortest connection between the center and the boundary. It is either the distance from the center to the perimeter (in the case of a circle), or the distance from the center to the surface (in the case of a sphere). It is half of the diameter.[2] That is, when r is the radius and d is the diameter:[3]

r = d ÷ 2

d = 2 x r = r + r

The relationship between the radius [math]{\displaystyle r}[/math] and the circumference [math]{\displaystyle c}[/math] of a circle is [math]~c = 2\pi r.[/math]

The area [math]{\displaystyle A}[/math] of a circle of radius [math]{\displaystyle r}[/math] is [math]{\displaystyle ~A = \pi r^2.}[/math]

Related pages


  1. "List of Geometry and Trigonometry Symbols" (in en-US). 2020-04-17. 
  2. Weisstein, Eric W.. "Radius" (in en).,equal%20to%20half%20the%20diameter.. 
  3. "Radius, diameter, & circumference | Circles (article)" (in en). 

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