 In geometry, a circumcircle of a given two-dimensional geometric shape is the smallest circle which contains the shape completely within it. Every bounded shape has a unique circumcircle. The center of this circumcircle is known as the shape's circumcenter. circumscribed circle made by myself File links The following pages link to this file: Circumcircle Categories: GFDL images ...
Geometry (from the Greek words Geo = earth and metro = measure) is the branch of mathematics first popularized in ancient Greek culture by Thales (circa 624-547 BC) dealing with spatial relationships. ...
Dimension (from Latin measured out) is, in essence, the number of degrees of freedom available for movement in a space. ...
In geometry, two sets of points are of the same shape precisely if one can be transformed to another by dilating (i. ...
In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, called the centre. ...
Cyclic polygons At least three vertices of a shape will lie on its circumcircle. A polygon whose vertices all lie on its circumcircle is said to be a cyclic polygon. All regular simple polygons, all triangles and all rectangles are cyclic. In geometry, a vertex (Latin: whirl, whirlpool; plural vertices) is a corner of a polygon (where two sides meet) or of a polyhedron (where three or more faces and an equal number of edges meet). ...
Wiktionary has a definition of: Polygon For other use please see Polygon (disambiguation) A polygon (literally many angle, see Wiktionary for the etymology) is a closed planar path composed of a finite number of sequential line segments. ...
A simple concave hexagon In geometry, two edges of a polygon may cross or even overlap in general. ...
For alternate meanings, such as the musical instrument, see triangle (disambiguation). ...
In geometry, a rectangle is a defined as a quadrilateral polygon in which all four angles are right angles. ...
Circumcircles of triangles The circumcircle of a triangle is the unique circle on which all its three vertices lie. (This is not the same as the first definition for "thin" triangles where only two points would lie on the first definition's circumcircle.) The circumcenter of a triangle can be found as the intersection of the three perpendicular bisectors. (A perpendicular bisector is a line that forms a right angle with one of the triangle's sides and intersects that side at its midpoint.) This is because the circumcenter is equidistant from any pair of the triangle's points, and all points on the perpendicular bisectors are equidistant from those points of the triangle. New version by Tarquin Made with Adobe Illustrator. ...
Perpendicular is a geometric term that may be used as a noun or adjective. ...
For the numerical analysis algorithm, see bisection method. ...
A triangle is acute (all angles smaller than a right angle) iff the circumcenter lies inside the triangle; it is obtuse (has an angle bigger than a right one) iff the circumcenter lies outside, and it is a right triangle iff the circumcenter lies on one of its sides (namely on the hypotenuse). This is one form of Thales' theorem. ↔ ⇔ ≡ For other possible meanings of iff, see IFF. In mathematics, philosophy, logic and technical fields that depend on them, iff is used as an abbreviation for if and only if. Although P iff Q is most standard, common alternative phrases include Q is necessary and sufficient for P and P...
For alternate meanings, such as the musical instrument, see triangle (disambiguation). ...
In geometry, Thales theorem (named after Thales of Miletus) states that if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ABC is a right angle. ...
 Wikipedia does not have an article with this exact name. ...
The diameter of the circumcircle can be computed as the length of any side of the triangle, divided by the sine of the opposite angle. (As a consequence of the law of sines, it doesn't matter which side is taken: the result will be the same.) The triangle's nine point circle has half the diameter of the circumcircle. For the geometric term, see diameter. ...
In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ...
This article is about angles in geometry. ...
In trigonometry, the law of sines (or sine law) is a statement about arbitrary triangles in the plane. ...
In geometry, the nine point circle is a circle that can be constructed for any given triangle. ...
The circumcenter always lies on one line with the triangle's centroid and orthocenter. This line is known as Euler's line. Centroid of a triangle In geometry, the centroid or barycenter of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane. ...
In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to (i. ...
In geometry, Eulers line (red line in the image) is the line passing through the orthocenter (blue), the circumcenter (green), the centroid (yellow), and the center of the nine point circle (red point) of any triangle. ...
The circumcenter's isogonal conjugate is the orthocenter. The isogonal conjugate of a point P with respect to a triangle ABC is constructed by reflecting the lines PA, PB, and PC about the angle bisectors of A, B, and C. These three reflected lines concur at the isogonal conjugate of P. Categories: Geometry stubs ...
In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to (i. ...
The useful minimum bounding circle of three points is defined either by the circumcircle (where three points are on the minimum bounding circle) or by the two points of the longest side of the triangle (where the two points define a diameter of the circle.). It is common to confuse the minimum bounding circle with the circumcircle.
The circumcircle of three collinear points is an infinitely large circle. Nearly collinear points often cause frequent problems and errors in computation of the circumcircle.
Circumcircles of triangles have an intimate relationship with the Delaunay triangularization of a set of points. In mathematics, and computational geometry, the Delaunay triangulation or Delone triangularization for a set P of points in the plane is the triangulation DT(P) of P such that no point in P is inside the circumcircle of any triangle in DT(P). ...
In mathematics, a set can be thought of as any well-defined collection of things considered as a whole. ...
Circumcircle equation The circumcircle is given by the equation where A, B and C are the points of the triangle, and the solution for v is the circumcircle. (Note A2 = Ax2 + Ay2.)
Given
- , , ,
we then have av2 − 2Sv − b = 0, and assuming the three points were not in a line (otherwise the circumcircle doesn't exist), (v − S)2 = b/a + S2/a2, giving the circumcenter S/a and the circumradius √(b/a + S2/a2). This approach should also work for the circumsphere of a tetrahedron. A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. ...
Circumcircle of circles See Descartes' theorem. In geometry, Descartes theorem establishes a relationship between four kissing, or mutually tangent, circles. ...
See also In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. ...
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