The nature of the inner, outer, center of gravity and perpendicularity of a triangle It's urgent

The nature of the inner, outer, center of gravity and perpendicularity of a triangle It's urgent

Heart: the intersection of the three bisectors, is also the center of the triangle inscribed circle
Property: equal distance to three sides
Outer center: the intersection of three vertical lines, also the center of the triangle circumcircle
Property: equal distance to three vertices
Center of gravity: the intersection of three central lines
Properties: the distance from the third bisector of the three midlines to the vertex is twice the distance to the midpoint of the opposite side
Perpendicularity: the point of intersection of three high lines
Property: this point is the product of two parts of each high line
Side center: the intersection of the bisector of the outer angle of any two corners of a triangle and the bisector of the inner angle of the third corner
Property: equal distance to three sides
Boundary Center: the intersection of a line passing through a vertex of a triangle and one side of the triangle
Properties: there are three boundary centers in a triangle. The three boundary centers intersect with three straight lines connected with their corresponding vertices at one point
Eurowire: the outer center, center of gravity, nine point circle center and vertical center of a triangle are successively located on the same straight line, which is called the eurowire of a triangle