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The term "concurrent" or "concurrency" is typically seen in geometry in relation to triangles. ancient Greek mathematicians knew that the existence of specific lines, i beg your pardon when drawn in relationship to a triangle, intersected in one common suggest inside the triangle. Once the first such line to be discovered, mathematicians thought that castle had discovered the "center" the the triangle. Upon further investigation, however, the was uncovered that there were other particular lines that additionally intersected in one common point inside the triangle, however these usual points did not coincide through the previously uncovered "center" point. All of the discovered typical points were considered to it is in "triangle centers" in the feeling that each of them might be described as the center of the triangle under certain conditions.
So, how countless "centers" walk a triangle possess? The Greeks knew of 3 such "centers", the centroid, the orthocenter, and also the circumcenter, described as the timeless triangle centers. End time, mathematicians have expanded the perform of "triangle centers" come contain end 100 entries.
It to be not till the eighteenth century the mathematician Leonhard Euler (1707-1783) discovered a relationship in between the three timeless triangle centers. Euler found that in any triangle, the centroid, orthocenter and circumcenter space collinear (they lie on the very same straight line).
In addition, the centroid is always located in between the orthocenter and also the circumcenter.
The distance from the centroid come the orthocenter is constantly twice the street from the centroid come the circumcenter.
The heat upon which these three classical triangle centers room collinear is dubbed the Euler line.
Note: The name "Euler" is pronounced as if it were spelled "Oiler" in English.
We will begin our examination with the three classic triangle centers: the centroid, the orthocenter, and the circumcenter. Us will additionally investigate the incenter.
Constructions because that each triangle center will be discussed, and also constructions for circumscribing and also inscribing a one in relation to a triangle.
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