Geodesic
On One Extremal Problem on the~Euclidean Plane
Matematičeskie trudy, Tome 4 (2001) no. 1, pp. 111-121.

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Given two intersecting congruent rectangles $P_1=ABCD$ and $P_2=EFGH$ in the Euclidean plane, let $L_1$ be the length of the part of the boundary $\partial P_1$ which lies in the interior $\operatorname{int}(P_2)$ of $P_2$ and similarly let $L_2$ be the length of the part of $\partial P_2$ which lies in the interior $\operatorname{int}(P_1)$ of $P_1$. The author solves J. W. Fickett's problem of validating the inequality $\frac13 L_1\le L_2\le 3L_1$. 
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Yu. V. Nikonorova. On One Extremal Problem on the~Euclidean Plane. Matematičeskie trudy, Tome 4 (2001) no. 1, pp. 111-121. http://geodesic.mathdoc.fr/item/MT_2001_4_1_a6/

[1] Croft H. T., Falconer K. J., Guy R. K., Unsolved Problems in Geometry, Springer-Verlag, Berlin, etc., 1994 | MR | Zbl

[2] Fickett J. W., “Overlapping congruent convex bodies”, Amer. Math. Monthly, 87 (1980), 814–815 | DOI | MR | Zbl