Vector expression of the four centers of a triangle: PA+PB+PC=0. The four centers of a triangle refer to its center of gravity, outer center, inner center and vertical center. If and only if the triangle is a regular triangle, the center of gravity, center of gravity, inner heart and outer heart are connected into a whole, which is called the center of a regular triangle.

Triangle is a closed figure composed of three line segments on the same plane but not on the same straight line, which has applications in mathematics and architecture. Ordinary triangles are divided into ordinary triangles (three sides are unequal) and isosceles triangles (isosceles triangles with unequal waist and equal waist and bottom).

Definition of "four centers": center of gravity: the intersection point of three sides' median lines, dividing the length of median lines into 2:1; Vertical center: the intersection of three high lines, which are perpendicular to the corresponding edges; Inner heart: the intersection of three bisectors (the center of inscribed circle), and the distance between any points on the bisectors is equal to both sides of the angle; Outer center: the intersection of three vertical lines (the center of the circumscribed circle), and the distance from the outer center to each vertex of the triangle is equal.

Vector calculation of four centers of triangle

Plane vector is the hot spot and focus of college entrance examination over the years, which is generally a mid-range multiple-choice question or a fill-in-the-blank question. The proposition highlights the basic operation and instrumentality of test vectors, and permeates the examination of core literacy such as mathematical operation and mathematical modeling.

In solving problems, it is often combined with trigonometric functions and the positional relationship between straight lines and conic curves. , mainly in the form of known conditions, involving vector * * * lines, product of quantities, etc.