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What are the hearts (such as the center of gravity) in mathematics? What is its essence? Come on, everybody, 3Q.
First of all, the center of the circumscribed circle of a triangle is simply called the center of the circle. Closely related to the center are the central angle theorem and the circular angle theorem. Second, the intersection of the three center lines of the triangle is called the center of gravity of the triangle. Mastering the center of gravity will divide each centerline into a fixed ratio of 2: 1 and the formula of centerline length, which is convenient for solving problems. Third, the joint of three tall vertical triangles 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 problems. Fourth, the center of the inscribed circle of the inner triangle is referred to as the heart. For the heart, to master the open angle formula, we should also remember the following extremely useful equivalence relations: Fifth, one bisector of the inner triangle intersects with the bisectors of the other two inner angles at a point, which is the bisector of the circumscribed circle. It's called Proximity. Proximity is often associated with the heart and is also closely related to the semi-circumference of a triangle. The theorem of center of gravity shows that the three median lines of a triangle intersect at one point. The distance from this point to the vertex is twice the distance from it to the midpoint of the opposite side. The above intersection point is called the center of gravity of the triangle. The perpendicular bisector of three sides of a triangle intersect at one point. This point is called the center of the triangle. The vertical center theorem of a triangle is called the vertical center of a triangle. The bisectors of the three internal angles of a triangle intersect at one point. This point is called the heart of a triangle. The transverse center theorem is called triangle and other bisectors. The bisector of the outer angle of two vertices intersects at a point, which is called the near center point of a triangle. A triangle has three minor centerlines. The center of gravity, epicenter, vertical center, heart and sub-center of a triangle are called the five centroids of the triangle. Are all important connection points of the triangle. Please accept them.