Thousands of years ago, when the Greek philosophers were laying the first foundations of geometry, someone was experimenting with triangles. They bisected two of the angles and noticed that the angle bisectors crossed. They drew the third bisector and surprised to find that it too went through the same point. They must have thought this was just a coincidence. But when they drew any triangle they discovered that the angle bisectors always intersect at a single point! This must be the 'center' of the triangle. Or so they thought.
After some experimenting they found other surprising things. For example the altitudes of a triangle also pass through a single point (the orthocenter). But not the same point as before. Another center! Then they found that the medians pass through yet another single point. Unlike, say a circle, the triangle obviously has more than one 'center'.
The points where these various lines cross are called the triangle's points of concurrency.
Located at intersection of the
Located at intersection of the perpendicular bisectors of the sides
||Located at intersection of the medians|
||Located at intersection of the altitudes|
In the case of an equilateral triangle, the incenter, circumcenter and centroid all occur at the same point.