Definition, Betydelse & Anagram | Engelska ordet CIRCUMCENTER

Definition av CIRCUMCENTER

1. cirkelcentrum

Exempel på hur man kan använda CIRCUMCENTER i en mening

• 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.
• Together with the centroid, circumcenter, and orthocenter, it is one of the four triangle centers known to the ancient Greeks, and the only one of the four that does not in general lie on the Euler line.
• The circumcenter is the point of intersection between the three perpendicular bisectors of the triangle's sides, and is a triangle center.
• The isogonal conjugate of the symmedian point is the third Centroid, and the isogonal conjugate of the orthocenter is the circumcenter.
• The orthocenter, the circumcenter, the centroid, the Exeter point, the de Longchamps point, and the center of the nine-point circle are collinear, all falling on a line called the Euler line.
• For incenter I, centroid G, circumcenter O, nine-point center N, and orthocenter H, we have for non-equilateral triangles the distance inequalities.
• A triangle that is itself equilateral has a unique isodynamic point, at its centroid(as well as its orthocenter, its incenter, and its circumcenter, which are concurrent); every non-equilateral triangle has two isodynamic points.
• Jeřábek hyperbola, a rectangular hyperbola centered on a triangle's nine-point circle and passing through the triangle's three vertices as well as its circumcenter, orthocenter, and various other notable centers.
• For example, the centroid, circumcenter, incenter and orthocenter were familiar to the ancient Greeks, and can be obtained by simple constructions.
• In a regular polygon, the incircle and the circumcircle are concentric—that is, they share a common center, which is also the center of the regular polygon, so the distance between the incenter and circumcenter is always zero.
• Thus, it is collinear with all the other triangle centers on the Euler line, which along with the orthocenter and circumcenter include the centroid and the center of the nine-point circle.
• If the triangle is equilateral, the circumcenter and symmedian coincide and therefore the Brocard circle reduces to a single point.
• The Brocard circle of the triangle is a circle having a diameter of the line segment between the circumcenter and symmedian.
• By Euler's theorem in geometry on the distance between the circumcenter and incenter of a triangle, two concentric circles (with that distance being zero) are the circumcircle and incircle of a triangle if and only if the radius of one is twice the radius of the other, in which case the triangle is equilateral.
• Other segments of interest in a triangle include those connecting various triangle centers to each other, most notably the incenter, the circumcenter, the nine-point center, the centroid and the orthocenter.
• The radii and centers of these circles are called inradius and circumradius, and incenter and circumcenter respectively.
• However, while the orthocenter and the circumcenter are in an acute triangle's interior, they are exterior to an obtuse triangle.
• Some of these points of intersection are standard; for instance, these include the construction of the centroid of a triangle as the point where its three median lines meet, the construction of the orthocenter as the point where the three altitudes meet, and the construction of the circumcenter as the point where the three perpendicular bisectors of the sides meet, as well as two versions of Ceva's theorem.
• Beyond the classical triangle centers (the circumcenter, incenter, orthocenter, and centroid) the book covers other centers including the Brocard points, Fermat point, Gergonne point, and other geometric objects associated with triangle centers such as the Euler line, Simson line, and nine-point circle.
• In fact, Euclid's Elements contains description of the four special points – centroid, incenter, circumcenter and orthocenter - associated with a triangle.

Förberedelsen av sidan tog: 294,84 ms.