Proportional relation of specific area. Mercedes-Benz theorem is a mathematical theorem, which describes the relationship between a point in a triangle and its area. This point is inside the triangle, and the line segment formed by the three vertices of the triangle divides the triangle into several parts, and the area of each part has a specific proportional relationship with the position of this point. The four centers of a triangle-center of gravity, inner heart, outer heart and hanging heart-all have their own unique properties. For example, if the center of gravity is the intersection of the midlines of three sides of a triangle, each midline of the triangle can be divided into two sections, so that the ratio of the lengths of the two sections is 2:1; The center is the intersection of the bisectors of the three internal angles of the triangle, and its distance to the three sides of the triangle is equal; The outer center is the intersection of the perpendicular lines of the three sides of the triangle, and its distance to the three vertices of the triangle is equal; The vertical center is the intersection of the heights of three sides of a triangle. When the point p in Mercedes theorem coincides with a center of a triangle, it will show a specific area proportion relationship. These relationships not only deepen our understanding of the four centers of the triangle, but also provide effective tools for solving problems related to the four centers of the triangle.