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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     author = {Yu. V. Nikonorova},
     title = {On {One} {Extremal} {Problem} on {the~Euclidean} {Plane}},
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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/