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Related to Orthocenter: Circumcenter


The point at which the altitudes of a triangle intersect.



the point of intersection of the three altitudes of a triangle. In any triangle the point of intersection of the medians, the center of a circumscribed circle, and the orthocenter all lie on one line.

References in periodicals archive ?
We also have proved that the orthogonal projection of the orthocenter of the Pavillet tetrahedron on the plane of its base triangle is the Gergonne point of its base triangle.
We generalized directly to 3D, and we defined the orthocenter as the point where the four altitudes of a tetrahedron intersect.
This work is presented with Cabri3D, [3]) Then, we made a conjecture that the orthocenter exists when at least one facet is an equilateral triangle.
Also, we proved that the four altitudes intersect with their opposite facet's orthocenter if the orthocenter exists.
In addition, we've also shown that all orthotetrahedrons (=tetrahedrons with orthocenter) have circumcenter, centroid, and orthocenter to be collinear.
cg3) containing the orthocenter of a right tetrahedron, 200;
cg3) containing the counterexample on conjectures for an orthocenter, 2007