On quadruples of orthopoles

Volenec, Vladimir; Jurkin, Ema; Horvath, Marija Šimić

doi:10.1007/s00022-023-00692-4

Cited by 4 publications

(9 citation statements)

References 4 publications

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“…In [1], we introduced the choice of a suitable coordinate system and placed a complete quadrangle in such a system. First, we will mention important definitions and statements proved in [1,2].…”

Section: Methodsmentioning

confidence: 99%

“…This is the fourth work in the series of such papers, and it considers the isoptic point of the complete quadrangle. In the second section, we provide an overview of the previously mentioned method and important points and circles, which were all introduced in previous papers [1][2][3]. In the third section, we present numerous results on the isoptic point of the complete quadrangle proved using our new method.…”

Section: Introductionmentioning

confidence: 99%

“…Our aim was to find a simple analytical tool with which it is possible to prove all of its properties using the same method. We have published several papers in this regard [1][2][3], where we present a unique method using rectangular coordinates that enables us to prove several properties of the complete quadrangle in a uniform way. This is the fourth work in the series of such papers, and it considers the isoptic point of the complete quadrangle.…”

Section: Introductionmentioning

confidence: 99%

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Isoptic Point of the Complete Quadrangle

Jurkin,

Horvath,

Volenec

2024

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In this paper, we study the complete quadrangle. We started this investigation in a few of our previous papers. In those papers and here, the rectangular coordinates are used to enable us to prove the properties of the rich geometry of a quadrangle using the same method. Now, we are focused on the isoptic point of the complete quadrangle ABCD, which is the inverse point to A′,B′,C′, and D′ with respect to circumscribed circles of the triangles BCD, ACD, ABD, and ABC, respectively, where A′,B′,C′, and D′ are isogonal points to A,B,C, and D with respect to these triangles. In studying the properties of the quadrangle regarding its isoptic point, some new results are obtained as well.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Isoptic Point of the Complete Quadrangle

Jurkin,

Horvath,

Volenec

2024

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“…This paper is the third in a series of such works. In [12] we introduced the choice of the suitable coordinate system that enables us to prove all the properties in the same way, while in [13] we focused on the center, anticenter and a diagonal triangle of the quadrangle, as well as on the isogonality with respect to the four triangles formed by the sides of the quadrangle. In this paper we give an overview of some properties of the quadrangle regarding the circles related to it.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we give an overview of some properties of the quadrangle regarding the circles related to it. Let us start by recalling some basic definitions and statements proved in [12] and [13].…”

Section: Introductionmentioning

confidence: 99%