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单词 Orthocenter
释义

orthocenter


The orthocenterMathworldPlanetmath of a triangleMathworldPlanetmath is the point of intersectionMathworldPlanetmath of its three heights.

In the figure, H is the orthocenter of ABC.

The orthocenter H lies inside, on a vertex or outside the triangle depending on the triangle being acute, right or obtuse respectively. Orthocenter is one of the most important triangle centersMathworldPlanetmath and it is very related with the orthic triangleMathworldPlanetmath (formed by the three height’s foots). It lies on the Euler lineMathworldPlanetmath and the four quadrilateralsMathworldPlanetmath FHDB,CHEC,AFHE are cyclic.

In fact,

  • A is the orthocenter of B,C,H;

  • B is the orthocenter of A,C,H;

  • C is the orthocenter of A,B,H.

The four points A,B,C, and H form what is calledan orthocentric tetrad.

Titleorthocenter
Canonical nameOrthocenter
Date of creation2013-03-22 11:55:41
Last modified on2013-03-22 11:55:41
OwnerMathprof (13753)
Last modified byMathprof (13753)
Numerical id11
AuthorMathprof (13753)
Entry typeDefinition
Classificationmsc 51-00
Related topicHeightOfATriangle
Related topicMedian
Related topicTriangle
Related topicEulerLine
Related topicOrthicTriangle
Related topicCEvasTheorem
Related topicCevasTheorem
Related topicCenterOfATriangle
Related topicIncenterMathworldPlanetmath
Related topicTrigonometricVersionOfCevasTheorem
Related topicCentroid
Definesorthocentric tetrad
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更新时间:2025/5/4 16:57:11