Tetraedru de volum 1

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Filip Chindea
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Tetraedru de volum 1

Post by Filip Chindea »

Se considera tetraedrul \( ABCD \) de volum \( 1 \) si punctele \( M, N, P, Q, R, S \) pe muchiile \( AB, CD, BC, DA, AC \) respectiv \( BD \). Daca \( MN, PQ \) si \( RS \) sunt concurente, aratati ca volumul poliedrului (acoperirii convexe) \( [M, N, P, Q, R, S] \) nu poate depasi \( 1/2 \).

[Flavian Georgescu, RMO Shortlist 2006, Clasa a VIII-a]
Last edited by Filip Chindea on Sun Mar 02, 2008 10:36 pm, edited 2 times in total.
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