Results 1 to 10 of about 59 (36)

Formulae connected with the Radii of the Incircle and the Excircles of a Triangle [PDF]

Proceedings of the Edinburgh Mathematical Society, 1893
The notation employed in the following pages is that recommended in a paper of mine on “The Triangle and its Six Scribed Circles”* printed in the first volume of the Proceedings of the Edinburgh Mathematical Society. It may be convenient to repeat all that is necessary for the present purpose.
J. S. Mackay
semanticscholar   +6 more sources

Cramer-Castillon on a Triangle's Incircle and Excircles

KoG
Cramer-Castillonov problem (CCP) se sastoji u traženju jednog ili više mnogokuta upisanih u kružnicu tako da njihove stranice ciklički prolaze kroz N točaka. Ovaj problem proučavamo u slučaju kada su točke vrhovi trokuta, a kružnica ili njegova upisana ili jedna od pripisanih kružnica.
Dominique Laurain, Peter Moses, Dan Reznik   +2 more
openaire   +2 more sources

74.31 Incircles and excircles of right-angled triangles

The Mathematical Gazette, 1990
Hiroshi Okumura
openaire   +3 more sources

Barycentric calculus in euclidean and hyperbolic geometry: a comparative introduction

, 2010
Euclidean Barycentric Coordinates The Classical Triangle Centers Triangle Incircle and Excircles Cartesian Models of Hyperbolic Geometry The Interplay of Einstein and Vector Addition Hyperbolic Barycentric Coordinates Hyperbolic Triangle Centers ...
A. Ungar
semanticscholar   +1 more source

Golden Ratio [PDF]

, 2021
This paper introduces the unique geometric features of 1:2:  right triangle, which is observed to be the quintessential form of Golden Ratio (φ). The 1:2:  triangle, with all its peculiar geometric attributes described herein, turns out to be the real ...
Rajput, Dr. Chetansing
core   +2 more sources

Triads of Conics Associated with a Triangle [PDF]

, 2022
Podsjećamo na konstrukcije temeljene na trijadama konika sa žarištima u parovima vrhova referetnog trokuta. Nalazimo da njihovih 6 vrhova leži na dobro poznatim konikama čiji tip analiziramo.
Garcia, Ronaldo, Gheorghe, Liliana G., Moses, Peter, Reznik, Dan   +3 more
core   +2 more sources

Area and perimeter relationship for different shapes with an inradius [PDF]

, 2022
In this paper, we show that an interesting relationship for a triangle, which is Area/Perimeter = r/2, extends to other shapes with an inradius r (i.e., shapes with an inscribed circle). These shapes include squares, circles, rhombuses, regular polygons,
Kaufman, Richard
core   +1 more source

Synthetic foundations of cevian geometry, III: The generalized orthocenter [PDF]

, 2015
In this paper, the third in the series, we define the generalized orthocenter $H$ corresponding to a point $P$, with respect to triangle $ABC$, as the unique point for which the lines $HA, HB, HC$ are parallel, respectively, to $QD, QE, QF$, where $DEF ...
Minevich, Igor, Morton, Patrick
core   +2 more sources

A family of hyperbolas associated to a triangle [PDF]

, 2019
In this note, we explore an apparently new one parameter family of conics associated to a triangle. Given a triangle we study ellipses whose one axis is parallel to one of sides of the triangle.
Zięba, Maciej
core   +1 more source

Euler’s inequality for the circumradius and inradius of a triangle [PDF]

, 2020
For any arbitrary triangle ABC, let R denote its circumradius and r its inradius (Figure 1). It was the Swiss-German mathematician Leonhard Euler who first observed that regardless of the shape of the triangle, the following inequality is invariably ...
Shirali, Shailesh
core