Geodesic
ANY CYCLIC QUADRILATERAL CAN BE INSCRIBED IN ANY CLOSED CONVEX SMOOTH CURVE
Forum of Mathematics, Sigma, Tome 6 (2018)

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We prove that any cyclic quadrilateral can be inscribed in any closed convex $C^{1}$ -curve. The smoothness condition is not required if the quadrilateral is a rectangle. 
@article{10_1017_fms_2018_7,
     author = {ARSENIY AKOPYAN and SERGEY AVVAKUMOV},
     title = {ANY {CYCLIC} {QUADRILATERAL} {CAN} {BE} {INSCRIBED} {IN} {ANY} {CLOSED} {CONVEX} {SMOOTH} {CURVE}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {6},
     year = {2018},
     doi = {10.1017/fms.2018.7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2018.7/}
}
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ARSENIY AKOPYAN; SERGEY AVVAKUMOV. ANY CYCLIC QUADRILATERAL CAN BE INSCRIBED IN ANY CLOSED CONVEX SMOOTH CURVE. Forum of Mathematics, Sigma, Tome 6 (2018). doi: 10.1017/fms.2018.7

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