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The Simson line of a vertex of the triangle is the altitude of the triangle dropped from that vertex, and the Simson line of the point diametrically opposite to the vertex is the side of the triangle opposite to that vertex. If P and Q are points on the circumcircle, then the angle between the Simson lines of P and Q is half the angle of the ...
The curved point-normal triangle, in short PN triangle, is an interpolation algorithm to retrieve a cubic Bézier triangle from the vertex coordinates of a regular flat triangle and normal vectors. The PN triangle retains the vertices of the flat triangle as well as the corresponding normals. For computer graphics applications, additionally a ...
Let ABC be any triangle. Let the Euler line of triangle ABC meet the sidelines BC, CA and AB of triangle ABC at D, E and F respectively. Let A g B g C g be the triangle formed by the Euler lines of the triangles AEF, BFD and CDE, the vertex A g being the intersection of the Euler lines of the triangles BFD and CDE, and similarly for the other two vertices.
Generalization for arbitrary triangles, green area = blue area Construction for proof of parallelogram generalization. Pappus's area theorem is a further generalization, that applies to triangles that are not right triangles, using parallelograms on the three sides in place of squares (squares are a special case, of course). The upper figure ...
In Euclidean geometry, the Droz-Farny line theorem is a property of two perpendicular lines through the orthocenter of an arbitrary triangle. Let T {\displaystyle T} be a triangle with vertices A {\displaystyle A} , B {\displaystyle B} , and C {\displaystyle C} , and let H {\displaystyle H} be its orthocenter (the common point of its three ...
Dry January is a challenge started in 2013 to eliminate alcohol from your diet. This is what you need to know about the health benefits.
(Reuters) -U.S. President-elect Donald Trump on Wednesday said he was picking Kari Lake, a former news anchor and a hardline Republican who failed to win an Arizona Senate seat last month, to be ...
In geometry, the Euler line, named after Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər), is a line determined from any triangle that is not equilateral.It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle.