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A triangle showing its circumcircle and circumcenter (black), altitudes and orthocenter (red), and nine-point circle and nine-point center (blue) In geometry, the nine-point center is a triangle center, a point defined from a given triangle in a way that does not depend on the placement or scale of the triangle.
The first published English grammar was a Pamphlet for Grammar of 1586, written by William Bullokar with the stated goal of demonstrating that English was just as rule-based as Latin. Bullokar's grammar was faithfully modeled on William Lily's Latin grammar, Rudimenta Grammatices (1534), used in English schools at that time, having been ...
The Gregg Reference Manual: A Manual of Style, Grammar, Usage, and Formatting is a guide to English grammar and style, written by William A. Sabin [1] and published by McGraw-Hill. The book is named after John Robert Gregg. The eleventh (“Tribute”) edition was published in 2010.
Examples of cyclic quadrilaterals. In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic.
The circumcenter's position depends on the type of triangle: For an acute triangle (all angles smaller than a right angle), the circumcenter always lies inside the triangle. For a right triangle, the circumcenter always lies at the midpoint of the hypotenuse. This is one form of Thales' theorem.
The word circumsphere is sometimes used to mean the same thing, by analogy with the term circumcircle. [2] As in the case of two-dimensional circumscribed circles (circumcircles), the radius of a sphere circumscribed around a polyhedron P is called the circumradius of P, [3] and the center point of this sphere is called the circumcenter of P. [4]