GEOS circle
In geometry, the GEOS circle is derived from the intersection of four lines that are associated with a generalized triangle: the Euler line, the Soddy line, the orthic axis and the Gergonne line. Note that the Euler line is orthogonal 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 X650 and X20 and passes through these points as well as the two points of orthogonal intersection.
The orthogonal intersection points are X468 and X1323.
The orthocentric system comprises X650, X20, X1375 and X3012.
The X point notation is the Clark Kimberling ETC classification of triangle centers.
