The nature of the center of gravity is 1. The ratio of the distance from the center of gravity to the vertex to the distance from the center of gravity to the midpoint is 2: 1.
2. The areas of the three triangles formed by the center of gravity and the three vertices of the triangle are equal.
3. The minimum distance from the center of gravity to the three vertices of the triangle.
4. In the plane rectangular coordinate system, the coordinate of the center of gravity is the arithmetic average of the vertex coordinates.
5. The center of gravity is the point where the product of the distances from the triangle to the three sides is the largest.
6. If the center of gravity of △ ABC is p and point G is any point in the triangle, then 3pg2 = (ga 2+gb 2+gc 2)-(ab 2+bc 2+ac 2)/3.
7. In triangle ABC, if the straight line passing through the center of gravity P intersects with the straight lines where AB and AC are located in D and E respectively, AB/AD+AC/AE=3.
8. Tangents are made from the three vertices of △ABC to the circle with the opposite side as the diameter. All six tangents are on the circle with the center of gravity O as the center and r =118 (AB+BC+AC) as the radius.
9.p is the center of gravity of the triangle ABC, and G is any point on the △ABC plane, so GA 2+GB 2+GC 2+PA 2+Pb 2+PC 2+3pg 2.
The definition of the center of gravity in mathematics generally refers to the center of gravity of a triangle.
The center of gravity of a triangle, the center of gravity of a triangle is the intersection of three midlines of a triangle. When the geometry is uniform, the center of gravity coincides with the centroid.
The center of gravity is the intersection of three sides of a triangle, and the intersection of three lines can be proved by dovetail theorem.
The center of gravity of other figures, the following geometry is uniform, line segments refer to thin rods, and plane figures refer to thin plates.
The center of gravity of a triangle is the intersection of three sides. The center of gravity of the line segment is the midpoint of the line segment.
The center of gravity of a parallelogram is the intersection of its two diagonals, and it is also the intersection of the midpoint connecting lines of two pairs of opposite sides.
The center of gravity of a parallelepiped is the intersection of its four diagonal lines, the intersection of the midpoint lines of six pairs of opposite sides, and the intersection of four pairs of opposite barycentric lines.
The center of gravity of a circle is the center of the circle, and the center of gravity of a ball is the center of the ball.
The center of gravity of the cone is the one closest to the bottom on the bisector connecting the vertex and the center of gravity of the bottom.
The center of gravity of tetrahedron is also the intersection point of the connecting line between each fixed point and the relative center of gravity, and also the intersection point of each side and the plane determined by the midpoint of the opposite side.
What is the intersection of the centers of gravity? The center of gravity of a triangle is the intersection of three midlines of three sides of the triangle. When the geometry is uniform, the center of gravity coincides with the centroid. The three midlines must intersect, and the intersection point is named the center of gravity; In the center of gravity segmentation, the ratio of line segment to line segment is two to one.
Center of gravity: the median lines of three sides intersect at one point; Vertical center: the three heights of a triangle (straight line) intersect at one point; Exterior center: the perpendicular lines of the three sides of a triangle intersect at one point; Inner heart: The bisectors of the three inner angles of a triangle intersect at one point.