Difference between revisions of "Diameter"
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A '''diameter''' of a [[circle]] is a [[chord]] of that circle which passes through the [[center]]. Thus a diameter divides the circle into two regions of equal [[area]] called [[semicircle]]s. | A '''diameter''' of a [[circle]] is a [[chord]] of that circle which passes through the [[center]]. Thus a diameter divides the circle into two regions of equal [[area]] called [[semicircle]]s. | ||
| − | {{asy image|<asy>unitsize( | + | {{asy image| |
| + | <asy> | ||
| + | unitsize(1cm); | ||
| + | draw(unitcircle,black); | ||
| + | pair O = (0,0); | ||
| + | pair A = (-1,0); | ||
| + | pair B = (1,0); | ||
| + | draw(A--O--B); | ||
| + | label("$O$",O,S); | ||
| + | label("$A$",A,W); | ||
| + | label("$B$",B,E); | ||
| + | </asy>|right|This circle has diameter <math>AB</math> since center <math>O</math> lies on <math>AB</math>.}} | ||
Revision as of 18:06, 16 January 2025
A diameter of a circle is a chord of that circle which passes through the center. Thus a diameter divides the circle into two regions of equal area called semicircles.
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  since center  lies on .
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![[asy] unitsize(1cm); draw(unitcircle,black); pair O = (0,0); pair A = (-1,0); pair B = (1,0); draw(A--O--B); label("$O$",O,S); label("$A$",A,W); label("$B$",B,E); [/asy]](http://latex.artofproblemsolving.com/d/7/b/d7bdbea548f34cc7f1df10c74145f32aa7ea11e8.png)
Diameter of a set
The diameter of more general sets can also be defined. In any given metric space (that is, anywhere you can measure distances between points such as normal Euclidean 3-D space, the surface of the Earth, or any real vector space) the diameter of a bounded set of points is the supremum of the distances between pairs of points. In the case where the set of points is a circle, the diameter is the length of the diameter of the circle.
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