Search results
Results from the WOW.Com Content Network
In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example, the centroid, circumcenter, incenter and orthocenter were familiar to the ancient Greeks, and can be obtained by simple constructions.
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 ...
The orthocenter H, the centroid G, the circumcenter O, and the center N of the nine-point circle all lie on a single line, known as the Euler line. [18] The center of the nine-point circle lies at the midpoint of the Euler line, between the orthocenter and the circumcenter, and the distance between the centroid and the circumcenter is half of ...
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.
Likewise, a triangle's circumcenter—the intersection of the three sides' perpendicular bisectors, which is the center of the circle that passes through all three vertices—falls inside an acute triangle but outside an obtuse triangle. The right triangle is the in-between case: both its circumcenter and its orthocenter lie on its boundary.
The circumcenter is the point of intersection between the three perpendicular bisectors of the triangle's sides, and is a triangle center. More generally, an n -sided polygon with all its vertices on the same circle, also called the circumscribed circle, is called a cyclic polygon , or in the special case n = 4 , a cyclic quadrilateral .
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 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