Pedal triangle: Difference between revisions
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In [[triangle geometry]], the '''pedal triangle''' is a further triangle defined with respect to a point in the interior of the original triangle. The '''pedal lines''' from a point are the three perpendiculars from that point to the edges of the triangle. The pedal triangle is defined by the three points of intersection. If the edges of the original triangle are produced, the definition makes sense for points outside the original triangle, provided only that they are not on the [[circumcircle]], in which case the three points lie on a '''Simson line'''.. | In [[triangle geometry]], the '''pedal triangle''' is a further triangle defined with respect to a point in the interior of the original triangle. The '''pedal lines''' from a point are the three perpendiculars from that point to the edges of the triangle. The pedal triangle is defined by the three points of intersection. If the edges of the original triangle are produced, the definition makes sense for points outside the original triangle, provided only that they are not on the [[circumcircle]], in which case the three points lie on a '''Simson line'''.. | ||
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==References== | ==References== | ||
* {{cite book | author=H.S.M. Coxeter | coauthors=S.L. Greitzer | title=Geometry revisited | series=New Mathematical Library | volume=19 | publisher=[[MAA]] | year=1967 | isbn=0-88385-619-0 }} | * {{cite book | author=H.S.M. Coxeter | coauthors=S.L. Greitzer | title=Geometry revisited | series=New Mathematical Library | volume=19 | publisher=[[MAA]] | year=1967 | isbn=0-88385-619-0 }}[[Category:Suggestion Bot Tag]] | ||
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Latest revision as of 11:00, 2 October 2024
In triangle geometry, the pedal triangle is a further triangle defined with respect to a point in the interior of the original triangle. The pedal lines from a point are the three perpendiculars from that point to the edges of the triangle. The pedal triangle is defined by the three points of intersection. If the edges of the original triangle are produced, the definition makes sense for points outside the original triangle, provided only that they are not on the circumcircle, in which case the three points lie on a Simson line..
The pedal triangle construction may be iterated with respect to the original point. The third iterated pedal triangle is similar to the original.
An example of a pedal triangle is the orthic triangle, which is the pedal triangle for the orthocentre.
References
- H.S.M. Coxeter; S.L. Greitzer (1967). Geometry revisited. MAA. ISBN 0-88385-619-0.