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49 relations: Acute and obtuse triangles, Altitude (triangle), Angle, Apollonian circles, Barnes & Noble, Charles Julien Brianchon, Circle, Circumconic and inconic, Circumscribed circle, Complete quadrangle, Concyclic points, Conic section, Cut-the-Knot, Cyclic quadrilateral, Ellipse, Euler line, Feuerbach point, Geometry, Holt McDougal, Homothetic center, Homothetic transformation, Hyperbola, Incircle and excircles of a triangle, Jean-Victor Poncelet, Johnson circles, Karl Wilhelm Feuerbach, Lester's theorem, Line segment, Medial triangle, Midpoint, Napoleon points, Nine-point center, Nine-point hyperbola, Olry Terquem, Orthocentric system, Orthopole, Paul R. Halmos – Lester R. Ford Award, Perpendicular, Point (geometry), Polar circle (geometry), Poncelet point, Synthetic geometry, Tangent circles, Tangential triangle, Triangle, Triangle center, Trilinear coordinates, Václav Jeřábek, Vertex (geometry).
Acute and obtuse triangles
An acute triangle is a triangle with all three angles acute (less than 90°).
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Altitude (triangle)
In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex).
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Angle
In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
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Apollonian circles
Apollonian circles are two families of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa.
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Barnes & Noble
Barnes & Noble, Inc., a Fortune 500 company, is the bookseller with the largest number of retail outlets in the United States, and a retailer of content, digital media, and educational products.
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Charles Julien Brianchon
Charles Julien Brianchon (19 December 1783 – 29 April 1864) was a French mathematician and chemist.
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Circle
A circle is a simple closed shape.
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Circumconic and inconic
In triangle geometry, a circumconic is a conic section that passes through the three vertices of a triangle, and an inconic is a conic section inscribed in the sides, possibly extended, of a triangle.
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Circumscribed circle
In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.
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Complete quadrangle
In mathematics, specifically projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting the six pairs of points.
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Concyclic points
In geometry, a set of points are said to be concyclic (or cocyclic) if they lie on a common circle.
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Conic section
In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.
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Cut-the-Knot
Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics.
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Cyclic quadrilateral
In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.
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Ellipse
In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.
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Euler line
In geometry, the Euler line, named after Leonhard Euler, is a line determined from any triangle that is not equilateral.
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Feuerbach point
In the geometry of triangles, the incircle and nine-point circle of a triangle are internally tangent to each other at the Feuerbach point of the triangle.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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Holt McDougal
Holt McDougal is an American publishing company, a division of Houghton Mifflin Harcourt, that specializes in textbooks for use in secondary schools.
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Homothetic center
In geometry, a homothetic center (also called a center of similarity or a center of similitude) is a point from which at least two geometrically similar figures can be seen as a dilation or contraction of one another.
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Homothetic transformation
In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number λ called its ratio, which sends in other words it fixes S, and sends any M to another point N such that the segment SN is on the same line as SM, but scaled by a factor λ. In Euclidean geometry homotheties are the similarities that fix a point and either preserve (if) or reverse (if) the direction of all vectors.
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Hyperbola
In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.
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Incircle and excircles of a triangle
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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Jean-Victor Poncelet
Jean-Victor Poncelet (1 July 1788 – 22 December 1867) was a French engineer and mathematician who served most notably as the Commanding General of the École Polytechnique.
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Johnson circles
In geometry, a set of Johnson circles comprises three circles of equal radius r sharing one common point of intersection H. In such a configuration the circles usually have a total of four intersections (points where at least two of them meet): the common point H that they all share, and for each of the three pairs of circles one more intersection point (referred here as their 2-wise intersection).
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Karl Wilhelm Feuerbach
Karl Wilhelm von Feuerbach (30 May 1800 – 12 March 1834) was a German geometer and the son of legal scholar Paul Johann Anselm Ritter von Feuerbach, and the brother of philosopher Ludwig Feuerbach.
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Lester's theorem
In Euclidean plane geometry, Lester's theorem states that in any scalene triangle, the two Fermat points, the nine-point center, and the circumcenter lie on the same circle.
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Line segment
In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.
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Medial triangle
The medial triangle or midpoint triangle of a triangle ABC is the triangle with vertices at the midpoints of the triangle's sides AB, AC and BC.
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Midpoint
In geometry, the midpoint is the middle point of a line segment.
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Napoleon points
In geometry, Napoleon points are a pair of special points associated with a plane triangle.
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Nine-point center
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.
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Nine-point hyperbola
In plane geometry with triangle ABC, the nine-point hyperbola is an instance of the nine-point conic described by Maxime Bôcher in 1892.
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Olry Terquem
Olry Terquem (16 June 1782 – 6 May 1862) was a French mathematician.
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Orthocentric system
In geometry, an orthocentric system is a set of four points on a plane, one of which is the orthocenter of the triangle formed by the other three.
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Orthopole
In geometry, the orthopole of a system consisting of a triangle ABC and a line ℓ in the same plane is a point determined as follows.
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Paul R. Halmos – Lester R. Ford Award
The Paul R. Halmos – Lester R. Ford Award (formerly known as the Lester R. Ford Award) is a $1,000 prize given annually by the Mathematical Association of America for authors of articles of expository excellence published in The American Mathematical Monthly or Mathematics Magazine.
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Perpendicular
In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).
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Point (geometry)
In modern mathematics, a point refers usually to an element of some set called a space.
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Polar circle (geometry)
In geometry, the polar circle of a triangle is the circle whose center is the triangle's orthocenter and whose squared radius is r^2 &.
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Poncelet point
In geometry, the Poncelet point of four given points is defined as follows: Let A, B, C, and D be four points in the plane that do not form an orthocentric system.
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Synthetic geometry
Synthetic geometry (sometimes referred to as axiomatic or even pure geometry) is the study of geometry without the use of coordinates or formulas.
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Tangent circles
In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point.
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Tangential triangle
In geometry, the tangential triangle of a reference triangle (other than a right triangle) is the triangle whose sides are on the tangent lines to the reference triangle's circumcircle at the reference triangle's vertices.
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Triangle
A triangle is a polygon with three edges and three vertices.
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Triangle center
In geometry, a triangle center (or triangle centre) is a point in the plane that is in some sense a center of a triangle akin to the centers of squares and circles, i.e. a point that is in the middle of the figure by some measure.
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Trilinear coordinates
In geometry, the trilinear coordinates x:y:z of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle.
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Václav Jeřábek
Václav Jeřábek (1845–1931) was a Czech mathematician, specialized in constructive geometry.
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Vertex (geometry)
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
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9 Point Circle, 9 point circle, 9-Point circle, 9-point circle, Euler's circle, Feuerbach Circle, Feuerbach circle, Feuerbach's Theorem, Feuerbach's Thoerem, Feuerbach's circle, Medial circle, Medioscribed circle, Nine point circle, Nine points circle, Nine-Point Circle, Nine-Points Circle, Orthic circle, Terquem's circle.
References
[1] https://en.wikipedia.org/wiki/Nine-point_circle
