(1) The point where the perpendicular lines of three sides of a triangle intersect is called the "outer center". If the outer center is the center of the circle and the distance from the outer center to the vertex of the triangle is the radius, the "circumscribed circle" of the triangle can be constructed.

(2) The point where the three center lines of a triangle intersect (that is, the straight line from the vertex to the midpoint of the opposite side) is called the "centroid", which is characterized in that as long as the supporting point is in the center of the triangle, it can be supported. The whole triangle, from which we can know that the center of gravity must be inside the triangle.

(3) The point where the bisectors of the three angles of a triangle intersect is called the center of the circle, and the inside of the triangle is inevitable. If the center of a triangle is the center and the distance from the center to the edge of the triangle is the radius, the triangle can be inscribed.

(4) The point where three heights of a triangle intersect is called the vertical center.

The outer center, center of gravity and vertical center are often on the same straight line of a triangle, which is the famous "Euler line".