they are all points of concurrency
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The Orthocenter The Centroid The Circumcenter The Incenter >.> 'nuff said
Yes, but only in an equilateral triangle.
When three or more lines intersect at one point, then they are considered concurrent.The four points of concurrence in triangles are the circumcenter, incenter, centroid, and orthocenter.
The orthocenter of a triangle is the point where the three altitudes of the triangle intersect. An altitude extends from a vertex (i.e. corner of the triangle) to the side opposite of it, and is perpendicular either to the side of the triangle, or to its extension. The three altitudes of a triangle are always concurrent (intersect at the same point). This point is known as the orthocenter, and always falls on the Euler Line with the centroid, circumcenter, and the center of the triangle's nine-point circle.
The centroid, orthocenter, and circumcenter of a triangle all lie on the Euler line; however, the incenter does not. The incenter, which is the intersection of the angle bisectors, represents the center of the triangle's incircle. Unlike the other three points, the incenter's position is influenced by the triangle's angles and side lengths, leading it to be generally located off the Euler line.