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The orthocenter (blue point), the center of the nine-point circle (red), the centroid (orange), and the circumcenter (green) all lie on a single line, known as Euler's line (red line). The center of the nine-point circle lies at the midpoint between the orthocenter and the circumcenter, and the distance between the centroid and the circumcenter ...
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
Download as PDF; Printable version; ... Concurrent lines; Adjacent angles; Central angle; ... Point location; Hidden line removal; History of geometry
The value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called the absolute value of the power of S; more precisely, it can be stated that: | | | | = | | | | = where r is the radius of the circle, and d is the distance between the center of the circle and the ...
In modern terms, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. [57] The size of an angle is formalized as an angular measure. In Euclidean geometry, angles are used to study polygons and triangles, as well as forming an object of study in their own right. [43]
The de Longchamps point is the point of concurrence of several lines with the Euler line. Three lines, each formed by drawing an external equilateral triangle on one of the sides of a given triangle and connecting the new vertex to the original triangle's opposite vertex, are concurrent at a point called the first isogonal center .
If the lines AB' and A'B are parallel and the lines BC' and B'C are parallel, then the lines CA' and C'A are parallel. (This is the affine version of Pappus's hexagon theorem). The full axiom system proposed has point, line, and line containing point as primitive notions: Two points are contained in just one line.
The angle formed by the symmedian and the angle bisector has the same measure as the angle between the median and the angle bisector, but it is on the other side of the angle bisector. The three symmedians meet at a triangle center called the Lemoine point. Ross Honsberger has called its existence "one of the crown jewels of modern geometry". [1]