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(2cm);draw(unitcircle,black);pair O = (0,0);pair A = (-1,0);pair B = (1,0);draw(A--O--B);label($O$,O);label($A$,A);label($B$,B);</asy>|right|This circle has diameter <math>AB</math> since center <math>O</math> lies on <math>AB</math>.}} | |
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[[Category:Definition]] | [[Category:Definition]] | ||
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Revision as of 18:00, 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.
unitsize(2cm);draw(unitcircle,black);pair O = (0,0);pair A = (-1,0);pair B = (1,0);draw(A--O--B);label($O$,O);label($A$,A);label($B$,B); (Error making remote request. Unknown error_msg) |
  since center  lies on .
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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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