In geometry, symmedians are three particular lines associated with every triangle. They are constructed by taking a median of the triangle (a line connecting...

geometry, the Lemoine point, Grebe point or symmedian point is the intersection of the three symmedians (medians reflected at the associated angle bisectors)...

through the same vertex, one obtains a symmedian. The three symmedians intersect in a single point, the symmedian point of the triangle. The sum of the...

the symmedian point X6 (also denoted by K) having trilinear coordinates a : b : c. So the Lemoine axis of △ABC is the trilinear polar of the symmedian point...

center of the nine-point circle X(6) Symmedian point intersection of the three symmedians X(7) Gergonne point symmedian point of contact triangle X(8) Nagel...

the three lines that are parallel to the edges that pass through its symmedian point. If the successive sides of a cyclic hexagon are a, b, c, d, e,...

line of the circumcenter and the symmedian point (i.e., the Brocard axis). The cubic passes through the centroid, symmedian point, both Fermat points, both...

orthocentroidal disk. Furthermore, the Fermat point, the Gergonne point, and the symmedian point are in the open orthocentroidal disk punctured at its own center...

}}\triangle ABC).} The isogonal conjugate of a triangle's centroid is its symmedian point. Any of the three medians through the centroid divides the triangle's...

Tangential quadrilateral Trapezoid Isosceles trapezoid Sangaku Straightedge Symmedian Tessellation Prototile Aperiodic tiling Wang tile Penrose tiling Trapezoid...

triangle. It was identified in 1836 by Christian Heinrich von Nagel as the symmedian point of the excentral triangle of the given triangle. The mittenpunkt...

circumcenter of the triangle. The isotomic conjugate of the orthocenter is the symmedian point of the anticomplementary triangle. Four points in the plane, such...

165  The center of perspectivity, where these three lines meet, is the symmedian point of the triangle. The tangent lines containing the sides of the tangential...

circumcentre O. The isogonal conjugate of the centroid G is (by definition) the symmedian point K. The isogonal conjugates of the Fermat points are the isodynamic...

\left([1+\cos(\alpha )]^{-1}:[1+\sec(\alpha )]^{-1}\right)\sim (\sec(\alpha ):1)} symmedian point ( σ + 1 σ + 2 : 1 σ + 2 ) ∼ ( σ + 1 : 1 ) {\displaystyle \left({\tfrac...

centroid G, the symmedian through the vertex is the reflection of the line AG in the bisector of the angle A. There are three symmedians for a triangle...

derived from a given triangle. It passes through the circumcenter and symmedian point of the triangle, and is centered at the midpoint of the line segment...

between the orthocenter and each vertex Symmedian point K a : b : c {\displaystyle a:b:c} Intersection of the symmedians – the reflection of each median about...

triangle, at the point where one of the three symmedians of the triangle cross its circumcircle. Each symmedian is the line through one vertex of the triangle...

of triangle △ABC is the centroid itself. The isotomic conjugate of the symmedian point is the third Brocard point, and the isotomic conjugate of the Gergonne...

the three lines that are parallel to the edges that pass through its symmedian point. There are two definitions of the hexagon that differ based on the...

These centers include the circumcenter, orthocenter, nine-point center, symmedian point, Gergonne point and Nagel point. Every Heronian triangle can be...

best known for his proof of the existence of the Lemoine point (or the symmedian point) of a triangle. Other mathematical work includes a system he called...

has coordinates s − a : s − b : s − c {\displaystyle s-a:s-b:s-c} . The symmedian point has coordinates a 2 : b 2 : c 2 {\displaystyle a^{2}:b^{2}:c^{2}}...

anticomplementary triangle and is also the isotomic conjugate of the symmedian point. It is center X(76) in the Encyclopedia of Triangle Centers. The...

Let ABC be any given triangle. Let O be the circumcenter and K be the symmedian point of triangle ABC. The circle with OK as diameter is the Brocard circle...

Michel Bataille, “Constructing a Triangle from Two Vertices and the Symmedian Point”, Forum Geometricorum 18 (2018), 129--133. Mitchell, Douglas W....

point of a triangle has a number of properties, including that it is the symmedian point of the Gergonne triangle. Trilinear coordinates for the vertices...

is the Fermat point. Thereafter, points now called nine-point center, symmedian point, Gergonne point, and Feuerbach point, to name a few, were added...

these six points of intersection lie on a conic. If P is chosen as the symmedian point, the resulting conic is a circle called the Lemoine circle. If the...