Synonymer & Information om | Engelska ordet CIRCUMCIRCLE

Exempel på hur man kan använda CIRCUMCIRCLE i en mening

• Every triangle whose base is the diameter of a circle and whose apex lies on the circle is a right triangle, with the right angle at the apex and the hypotenuse as the base; conversely, the circumcircle of any right triangle has the hypotenuse as its diameter.
• This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic.
• The sum of the perpendiculars from a regular n-gon's vertices to any line tangent to the circumcircle equals n times the circumradius.
• A polygon whose vertices are concyclic is called a cyclic polygon, and the circle is called its circumscribing circle or circumcircle.
• In coastal navigation, a triangle's circumcircle is sometimes used as a way of obtaining a position line using a sextant when no compass is available.
• For example, the isogonal conjugate of a line is a circumconic; specifically, an ellipse, parabola, or hyperbola according as the line intersects the circumcircle in 0, 1, or 2 points.
• An "external" version of this theorem, where the incircle is replaced by an excircle and the two additional circles are external to the circumcircle, is found in Shay Gueron (2002).
• 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.
• The Steiner circle of a triangle is concentric with the nine-point circle and has radius 3/2 the circumradius of the triangle; the de Longchamps point is the homothetic center of the Steiner circle and the circumcircle.
• 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.
• By comparison the circumcircle of a triangle is another circumconic that touches the triangle at its vertices, but is not centered at the triangle's centroid unless the triangle is equilateral.
• In Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle.
• The Borda–Carnot equation in fluid dynamics and several theorems in geometry are named after him: one that describes a property of the incircle and the circumcircle of triangle, one that describes a relation between triangles and conic sections and one that describes a property of certain perpendiculars on triangle sides.
• For example, the Trilinear polar of a point on the circumcircle must pass through its perspector, the Symmedian point X(6).
• All right kites are bicentric quadrilaterals (quadrilaterals with both a circumcircle and an incircle), since all kites have an incircle.
• The reference triangle's circumcircle, its nine-point circle, its polar circle, and the circumcircle of the tangential triangle are coaxal.
• In geometry, the incenter–excenter lemma is the theorem that the line segment between the incenter and any excenter of a triangle, or between two excenters, is the diameter of a circle (an incenter–excenter or excenter–excenter circle) also passing through two triangle vertices with its center on the circumcircle.
• In this example, the size of the vertex figure was chosen so that its circumcircle lies on the intersphere of the cuboctahedron, which also becomes the intersphere of the dual rhombic dodecahedron.
• Carnot's theorem (inradius, circumradius), describing a property of the incircle and the circumcircle of a triangle.
• The Nagel point lies on the curve since its isogonal conjugate is the point of concurrency of the lines joining the vertices and the opposite Mixtilinear incircle touchpoints, also the in-similitude of the incircle and the circumcircle.

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