from The American Heritage® Dictionary of the English Language, 4th Edition

  • n. The point of intersection of the three altitudes of a triangle.

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. : the intersection of the three lines that can be drawn flowing from the three corners of a triangle to a point along the opposite side where each line intersects that side at a 90 degree angle; in an acute triangle, it is inside the triangle; in an obtuse triangle, it is outside the triangle.

from the GNU version of the Collaborative International Dictionary of English

  • n. That point in which the three perpendiculars let fall from the angles of a triangle upon the opposite sides, or the sides produced, mutually intersect.

from The Century Dictionary and Cyclopedia

  • n. The cointersection point of the straight lines through the three vertexes of a triangle perpendicular to the opposite sides.


Sorry, no etymologies found.


  • The first is called the orthocenter, and is the intersection of the lines from each vertex that meet the opposing sides perpendicularly, which are called the altitudes.


  • In 1767 Leonhard Euler proved that for all triangles the orthocenter, the circumcenter, the centroid and the center of the midcircle are always on the same line.


  • Yet not until 1820, when a paper ∗ published by Brianchon and Poncelet appeared, were the remaining three points (the midpoints of the segments from the orthocenter to the vertices) found to be on this circle.

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  • Geometric Wonders 185 C B 'A' A B C 'F Figure 5. 23b With H as the orthocenter (the point of intersection of the altitudes), M is the midpoint of CH (see Figure 5.23d).

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  • These nine points, for any given triangle, are • The midpoints of the sides • The feet of the altitudes • The midpoints of the segments from the orthocenter to the vertices Have your students do the necessary construction to locate each of these nine points.

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  • Theorem In any triangle, the midpoints of the sides, the feet of the altitudes, and the midpoints of the segments from the orthocenter to the vertices lie on a circle.

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