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A nine-point circle bisects a line segment going from the corresponding triangle's orthocenter to any point on its circumcircle. Figure 4. The center N of the nine-point circle bisects a segment from the orthocenter H to the circumcenter O (making the orthocenter a center of dilation to both circles): [6]: p.152
According to Lester's theorem, the nine-point center lies on a common circle with three other points: the two Fermat points and the circumcenter. [9] The Kosnita point of a triangle, a triangle center associated with Kosnita's theorem, is the isogonal conjugate of the nine-point center. [10]
Common nine-point circle, where N, O 4, A 4 are the nine-point center, circumcenter, and orthocenter respectively of the triangle formed from the other three orthocentric points A 1, A 2, A 3. The center of this common nine-point circle lies at the centroid of the four orthocentric points. The radius of the common nine-point circle is the ...
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.
A clade is by definition monophyletic, meaning that it contains one ancestor which can be an organism, a population, or a species and all its descendants. [ note 1 ] [ 10 ] [ 11 ] The ancestor can be known or unknown; any and all members of a clade can be extant or extinct.
In Euclidean geometry with triangle ABC, the nine-point hyperbola is an instance of the nine-point conic described by American mathematician Maxime Bôcher in 1892. The celebrated nine-point circle is a separate instance of Bôcher's conic: Given a triangle ABC and a point P in its plane, a conic can be drawn through the following nine points:
In biology, a biological life cycle (or just life cycle when the biological context is clear) is a series of stages of the life of an organism, that begins as a zygote, often in an egg, and concludes as an adult that reproduces, producing an offspring in the form of a new zygote which then itself goes through the same series of stages, the ...
"Point centromeres" bind to specific proteins that recognize particular DNA sequences with high efficiency. Any piece of DNA with the point centromere DNA sequence on it will typically form a centromere if present in the appropriate species. The best characterized point centromeres are those of the budding yeast, Saccharomyces cerevisiae ...