Difference between revisions of "Circle"

 
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==Definition==
 
==Definition==
 
*The [[locus]] of points distance <math>\displaystyle {r}</math>(radius) from center <math>{O}</math>
 
*The [[locus]] of points distance <math>\displaystyle {r}</math>(radius) from center <math>{O}</math>
*A cross section of a cone or cylinder parallel to the base. For more on this, see [[Dandelin Spheres]], a commonly used method of deriving all [[conic sections]].
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*A cross section of a cone or cylinder parallel to the base. For more on this, see [[Dandelin Spheres]], a commonly used method of deriving all [[Conic sections]].
 
*<math>(x - a)^{2} + (y - b)^{2} = r^{2} </math> for a circle centered at <math>(a,b)</math> with radius <math>{r}</math>
 
*<math>(x - a)^{2} + (y - b)^{2} = r^{2} </math> for a circle centered at <math>(a,b)</math> with radius <math>{r}</math>
  
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*[http://www.artofproblemsolving.com/Forum/viewtopic.php?p=423848#p423848 2006 AMC 12A #21]
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?p=423848#p423848 2006 AMC 12A #21]
  
=== See Also ===
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== See Also ==
 
*[[Pi]]
 
*[[Pi]]
 
*[[Power of a point]]
 
*[[Power of a point]]

Revision as of 18:06, 19 June 2006

Definition

  • The locus of points distance $\displaystyle {r}$(radius) from center ${O}$
  • A cross section of a cone or cylinder parallel to the base. For more on this, see Dandelin Spheres, a commonly used method of deriving all Conic sections.
  • $(x - a)^{2} + (y - b)^{2} = r^{2}$ for a circle centered at $(a,b)$ with radius ${r}$

Formulas

  • Area $\displaystyle \pi r^2$
  • circumference $\displaystyle 2\pi r$

Other Properties

  • The perpendicular bisector of any chord in the circle is a diameter
  • awaiting diagrams to add stuff on inscribed angles + tangents.

Practice Problems

See Also

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