The center of the circumscribed circle of the triangle is called the epicenter for short.

Second, the center of gravity

The intersection of the three center lines of a triangle is called the center of gravity of the triangle.

The midline is divided into a fixed ratio of 2: 1 and a midline length formula, which is convenient for solving problems.

Third, look down.

The joint of three heights of a triangle is called the vertical center of the triangle. Four equilateral (circumscribed) circular triangles caused by the vertical center of the triangle provide great convenience for us to solve the problem.

Fourth, the heart.

The center of the inscribed circle of a triangle is called the heart for short. For the heart, to master the formula of opening angle, we must also remember the following extremely useful equivalence relations:

Fifth, the heart.

The bisector of the inner corner of the triangle intersects with the bisector of the outer corner of the other two inner corners at

A point is the center of a tangent circle, which is called the lateral center. The lateral center is usually associated with the heart.

The imitation center is also closely related to the half circumference of a triangle.

The center of gravity theorem The three midlines of a triangle intersect at a point, and the distance from the point to the vertex is twice as long as the distance from the midpoint of the opposite side to the vertex.

The intersection above is called the center of gravity of the triangle.

Eccentricity Theorem The perpendicular bisector of three sides of a triangle intersects at one point.

This is called the outer center of a triangle.

The vertical center theorem The three heights of a triangle intersect at one point.

This is called the center of the triangle.

Internal Theorem The bisectors of three internal angles of a triangle intersect at one point.

This is called the heart of a triangle.

Proximity Theorem The bisector of the inner angle and the bisector of the outer angle of a triangle intersect at the other two vertices.

This is called the center of mass of a triangle. A triangle has three centers of mass.

The center of gravity, outer center, vertical center, inner center and lateral center of a triangle are called the five centers of the triangle. Are all important connection points of the triangle.