Feuerbach point (category Theorems about triangles and circles) that the nine-point circle is tangent to the three excircles of the triangle as well as its incircle. A very short proof of this theorem based on Casey's... 9 KB (1,101 words) - 17:51, 7 January 2023 |
Bankoff circle Circular triangle Reuleaux triangle Circumcircle Disc Incircle and excircles of a triangle Nine-point circle Circular sector Circular segment... 5 KB (412 words) - 15:37, 5 April 2024 |
on the tangency of the nine-point circle of a triangle with its incircle and excircles Descartes' theorem Ford circle Bankoff circle Archimedes' twin circles... 3 KB (358 words) - 15:28, 5 February 2022 |
Outline of geometry (category Outlines of mathematics and logic) Circle List of circle topics Thales' theorem Circumcircle Concyclic Incircle and excircles of a triangle Orthocentric system Monge's theorem Power center Nine-point... 13 KB (912 words) - 16:57, 1 March 2024 |
List of circle topics (category Outlines of mathematics and logic) Great circle Great-circle distance Circle of a sphere Horocycle Incircle and excircles of a triangle Inscribed circle Johnson circles Magic circle (mathematics)... 9 KB (696 words) - 14:58, 22 March 2024 |
Greek mathematics (section Origins and etymology) Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly from the 5th century... 35 KB (3,652 words) - 02:23, 8 May 2024 |
Right triangle (section Circumcircle and incircle) the radii of the incircle and the three excircles: a + b + c = r + r a + r b + r c . {\displaystyle a+b+c=r+r_{a}+r_{b}+r_{c}.} Acute and obtuse triangles... 18 KB (2,951 words) - 21:06, 17 April 2024 |
Olry Terquem (section Education and career) to the incircle and excircles of a triangle. Terquem's other contributions to mathematics include naming the pedal curve of another curve, and counting... 9 KB (956 words) - 23:53, 13 December 2023 |
Triangle (section Similarity and congruence) with its incircle. The extouch triangle of a reference triangle has its vertices at the points of tangency of the reference triangle's excircles with its... 56 KB (8,656 words) - 02:58, 14 February 2024 |
Euclid (section Identity and historicity) Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the... 44 KB (4,312 words) - 03:57, 25 April 2024 |
Squaring the circle (category Compass and straightedge constructions) of a given circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether... 44 KB (4,817 words) - 19:02, 10 May 2024 |
List of triangle topics (category Outlines of mathematics and logic) points Hyperbolic triangle (non-Euclidean geometry) Hypotenuse Incircle and excircles of a triangle Inellipse Integer triangle Isodynamic point Isogonal... 11 KB (632 words) - 15:28, 30 April 2024 |
Problem of Apollonius (section Resizing and inversion) solutions to the general LLL problem (the incircle and excircles of the triangle formed by the three lines). Points and lines may be viewed as special cases... 99 KB (12,221 words) - 22:00, 2 May 2024 |
for all Heronian triangles, but additionally the centers of the incircle and excircles are at lattice points.: Thm. 5 See also Integer triangle § Heronian... 40 KB (5,843 words) - 20:14, 7 May 2024 |
Triangle conic (section Conics of Thomson and Darboux) the plane of the reference triangle and associated with it in some way. For example, the circumcircle and the incircle of the reference triangle are triangle... 15 KB (1,379 words) - 17:40, 7 April 2024 |
titled Volume I, From Thales to Euclid and Volume II, From Aristarchus to Diophantus. It got positive reviews and is still used today. Ten years later,... 13 KB (1,521 words) - 16:29, 13 June 2023 |
result is that the incircles can be exchanged for the excircles to the same triangles (tangent to the sides of the quadrilateral and the extensions of... 34 KB (4,964 words) - 22:53, 13 February 2023 |
incircle. Further important inellipses are the Steiner inellipse, which touches the triangle at the midpoints of its sides, the Mandart inellipse and... 14 KB (3,437 words) - 18:55, 30 March 2024 |
Incenter (section Definition and construction) those that have an incircle that is tangent to each side of the polygon. In this case the incenter is the center of this circle and is equally distant... 15 KB (2,072 words) - 10:39, 25 January 2024 |
triangle, and its center is the center of mass of the perimeter of the triangle.) Any vertex, the tangency of the opposite side with the incircle, and the Gergonne... 18 KB (2,579 words) - 03:53, 24 April 2024 |
Leon (Greek: Λέων) was an Ancient Greek mathematician and pupil of Neocleides, who was active from around 370 to 340 BCE. His book Elements was overshadowed... 2 KB (210 words) - 16:21, 7 October 2023 |
Spieker circle (section Nagel points and lines) In geometry, the incircle of the medial triangle of a triangle is the Spieker circle, named after 19th-century German geometer Theodor Spieker. Its center... 7 KB (769 words) - 22:36, 28 January 2024 |
semiperimeter also applies to tangential quadrilaterals, which have an incircle and in which (according to Pitot's theorem) pairs of opposite sides have... 6 KB (890 words) - 18:19, 18 April 2024 |
Circle (section Symbolism and religious use) circle of infinite radius. In every triangle a unique circle, called the incircle, can be inscribed such that it is tangent to each of the three sides of... 43 KB (5,861 words) - 18:20, 7 May 2024 |