Add to ORKGWe consider the problem of determining for which central points X of the triangle ABC the products of lengths of sides and cevians of X will be sides of a triangle. We shall prove that twenty-seven out of hundred and one central points from the Kimberling\u27s list have this property. The algebraic method of proof for this result is also used to obtain some new examples of three segments that are sides of a triangle and are built from elements of a given triangle
The cubic in an isotropic plane which passes through the intersections of the sides of an orthic tri...
Abstract. We show that the cevian triangles of certain triangle centers have perimeters not exceedin...
We obtain several characterizations of the Kiepert, Jarabek, and Feuerbach hyperbolas of a tringle A...
For a given triangle T and a real number ρ we define Ceva’s triangle Cρ(T) to be the triangle formed...
We give synthetic proofs of new results in triangle geometry, focusing especially on fixed points of...
The locus of points that determine a constant product of their distances to the sides of a triangle ...
Podsjećamo na konstrukcije temeljene na trijadama konika sa žarištima u parovima vrhova referetnog t...
In this note, we explore an apparently new one parameter family of conics associated to a triangle. ...
Famous construction of Fermat-Toricelly point of a triangle leads to the question is there a similar...
The article observes a one-parameter triangle family T . We prove that the sets of the orthocenters,...
We study the existence of equilateral triangles of given side lengths and with integer coordinates i...
In this article, we introduce an algorithm for automatic generation and categorization of triangle g...
Let ABC be a triangle with an interior point P. Let AP, BP, and CP intersect BC, AC, and AB at A', B...
Kažemo da je lik F poseban za trokut T ukoliko F može biti dobiven iz T korištenjem ravnala i šestar...
In this paper, the third in the series, we study the properties of the generalized orthocenter H cor...
The cubic in an isotropic plane which passes through the intersections of the sides of an orthic tri...
Abstract. We show that the cevian triangles of certain triangle centers have perimeters not exceedin...
We obtain several characterizations of the Kiepert, Jarabek, and Feuerbach hyperbolas of a tringle A...
For a given triangle T and a real number ρ we define Ceva’s triangle Cρ(T) to be the triangle formed...
We give synthetic proofs of new results in triangle geometry, focusing especially on fixed points of...
The locus of points that determine a constant product of their distances to the sides of a triangle ...
Podsjećamo na konstrukcije temeljene na trijadama konika sa žarištima u parovima vrhova referetnog t...
In this note, we explore an apparently new one parameter family of conics associated to a triangle. ...
Famous construction of Fermat-Toricelly point of a triangle leads to the question is there a similar...
The article observes a one-parameter triangle family T . We prove that the sets of the orthocenters,...
We study the existence of equilateral triangles of given side lengths and with integer coordinates i...
In this article, we introduce an algorithm for automatic generation and categorization of triangle g...
Let ABC be a triangle with an interior point P. Let AP, BP, and CP intersect BC, AC, and AB at A', B...
Kažemo da je lik F poseban za trokut T ukoliko F može biti dobiven iz T korištenjem ravnala i šestar...
In this paper, the third in the series, we study the properties of the generalized orthocenter H cor...
The cubic in an isotropic plane which passes through the intersections of the sides of an orthic tri...
Abstract. We show that the cevian triangles of certain triangle centers have perimeters not exceedin...
We obtain several characterizations of the Kiepert, Jarabek, and Feuerbach hyperbolas of a tringle A...