Orthocenter - The Point of concurrency of 3 Altitudes of a Triangle
Orthocenter, Centroid, Incenter and Circumcenter are the four most commonly talked about centers of a triangle. I have written a great deal about the Incenter, the Circumcenter and the Centroid in my previous posts. In this post, I will be specifically writing about the Orthocenter. Orthocenter is the point in the plane of a triangle where all three altitudes of the triangle intersect. An altitude of a triangle is the segment from a vertex perpendicular to the side opposite to the vertex, or perpendicular to the line that contains the opposite side. In the figure below, AD is the altitude from vertex A perpendicular to BC(or the line containing the side BC), the side sitting opposite of vertex A, of △ABC. Similarly, BE and DF are the other two altitudes of triangle ABC emanating from vertices B and C. All three altitudes intersect at point H - the Orthocenter of the triangle. In any triangle, the three altitudes are always concurrent(intersecting at a singl...