- GEOS circle
In
geometry , the GEOS circle is derived from the intersection of four lines that are associated with a generalizedtriangle : theEuler line , theSoddy line , theorthic axis and theGergonne line . Note that the Euler line isorthogonal to the orthic axis and that the Soddy line is orthogonal to the Gergonne line.These four lines provide six points of intersection of which two points occur at line intersections that are orthogonal. Consequently the other four points form an
orthocentric system .The GEOS circle is that circle centered at a point equidistant from "X"650 (the intersection of the orthic axis with the Gergonne line) and "X"20 (the intersection of the Euler line with the Soddy line and is known as the
de Longchamps point ) and passes through these points as well as the two points of orthogonal intersection.The orthogonal intersection points are "X"468 (the intersection of the orthic axis with the Euler line) and "X"1323 (the intersection of the Gergonne line with the Soddy line and is known as the
Fletcher point ).The orthocentric system comprises "X"650, "X"20, "X"1375 (the intersection of the Euler line with the Gergonne line and is known as the
Evans point ) and "X"3012 (the intersection of the Soddy line and the orthic axis).The "X"("i") point notation is the Clark Kimberling ETC classification of
triangle centers.References
*
* Clark Kimberling, " [http://faculty.evansville.edu/ck6/encyclopedia/ETC.html Encyclopedia of triangle centers] ". "(Lists some 3000 interesting points associated with any triangle.)"
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