# ON THE EXISTENCE OF INSCRIBED POLYGONS

• Lim, So Yeon (Department of Mathematics, Chonnam National University) ;
• Jin, Hong Sung (Department of Mathematics, Chonnam National University) ;
• Lee, Kwang Seuk (Yeosu Munsoo Middle School) ;
• Park, Myeongsoo (Department of Mathematics, Chonnam National University) ;
• Kim, Dong-Soo (Department of Mathematics, Chonnam National University)
• Accepted : 2017.11.15
• Published : 2018.03.25
• 165 5

#### Abstract

We consider the existence problem of inscribed n-gons ($n{\geq}5$) in a circle and find a necessary condition on exterior angles $a_1,\;{\cdots},\;a_n$ of an inscribed n-gon. Conversely, we show that this condition is sufficient for an inscribed polygon with exterior angles $a_1,\;{\cdots},\;a_n$ in this cyclic order to exist.

#### Keywords

existence;inscribed polygon;exterior angle

#### References

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2. G. Michelacci, Inscribed polygons and fixed points of homeomorphisms on the circle, Geom. Dedicata 40(1) (1991), 103-110. https://doi.org/10.1007/BF00181655
3. P. Schreiber, On the existence and constructibility of inscribed polygons, Beitrage zur Algebra und Geometrie 34(2) (1993), 195-199.