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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
In the case when the touching conic is unique, we find out its type.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:In this note, we study a chain of circles whose pairwise intersection points, taken in a certain order, also lie on two circles.
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Temel Bulgular & Veri:We give a short elementary proof of the following fact.
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Sonuç & Katkı:In the case when the touching conic is unique, we find out its type.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Chain of circles · Dao's theorem · Miquel's theorem
Abstract
In this note, we study a chain of circles whose pairwise intersection points, taken in a certain order, also lie on two circles. We give a short elementary proof of the following fact. There exists a conic which touches each line connecting the centres of adjacent circles of such chain. In the case of six circles of the chain, this means that the centres of these circles form a Brianchon hexagon. We consider all cases of the possible radically distinct positions of the original chain of circles. In the case when the touching conic is unique, we find out its type.
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Bu Makaleye Atıf Yap
G.HORVÁTH, Á. (2022). A Note on Centres in a Chain of Circles. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 226–230. https://ajindex.com/articles/539578