Trigonometry/Circles and Triangles/Orthocentric points
As previously noted, the altitudes of any triangle ABC intersect at their orthocentre, H.
The orthocentres of the triangles ABH, BCH, ACH are respectively C, A and B.
The four triangles ABC, ABH, BCH and ACH have the same nine-point circle. The four incircles and twelve excircles all touch this nine-point circle.
All four triangles have the same circumradius.
The reflection of H in any side of ABC lies on the circumcircle of ABC, and the same applies to each of the points A, B and C.
The centroids of the four triangles form a set of four points which is similar to the original set ABCH, but one third the size.Last modified on 10 April 2011, at 17:32