Center: The center of a circle.

Heart-shaped: the intersection of the center of a triangle inscribed with three bisectors.

Exterior center: the center of a triangle is round, the distances to the three angles are equal, and the perpendicular lines of the three sides intersect.

Vertical center: the intersection of three high lines of a triangle.

Center of gravity: the intersection of the median lines of three sides of a triangle.

Center: The intersection of three lines of an equilateral triangle (angle bisector, middle vertical line and high line). The so-called projection of three points (inner center, outer center and center of gravity) is orthographic projection.

Among them, the vertical foot from a point to a straight line is called the orthogonal projection of the point on this straight line. The line segment between the orthographic projections of two endpoints of a line segment on a straight line is called the orthographic projection of the line segment on the straight line.

From the similar nature of triangles:

Theorem In a right triangle, the height on the hypotenuse is the proportional average of the projections of two right angles on the hypotenuse. Each right-angled edge is the median of the projection of this right-angled edge on the hypotenuse and the proportion of the hypotenuse.