The centroid (G) of a triangle is the point of intersection of the three medians of the triangle. A median is a segment constructed from a vertex to the midpoint of the subtending side of the triangle.
The orthocenter (I) of a triangle is the point of intersection of the three altitudes of the triangle. An altitude is a line constructed from a vertex to the subtending side of the triangle and is perpendicular to that side. It should be noted that the orthocenter, in different cases, may lie outside the triangle; in these cases, the altitudes extend beyond the sides of the triangle.
The circumcenter (H) of a triangle is the point of intersection of the three perpendicular bisectors of the triangle. A perpendicular bisector is a line constructed at the midpoint of a side of a triangle at a right angle to that side. It should be noted that the circumcenter, in different cases, may lie outside the triangle; in these cases, the perpendicular bisectors extend beyond the sides of the triangle.
The three centers lie on same line.This is named after great Mathematician Euler.
