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Inegalitate in tetraedru 1
Posted: Sun Jan 18, 2009 6:41 pm
by Marius Mainea
In tetraedrul \( VABCD \) avem \( VC\perp AB \). Fie \( BM\perp VC \) si \( MN\perp AB \) , unde \( M\in (VC) \) si \( N\in (AB) \). Sa se demonstreze ca \( MN< CN \)
Posted: Wed Dec 16, 2009 5:41 pm
by Marius Mainea
Indicatie: \( VC\perp(ABM) \)
Posted: Wed Jan 13, 2010 6:19 pm
by Andi Brojbeanu
\( BM\perp VC\Rightarrow VC\perp BM \).
Din \( VC\perp BM \) si \( VC\perp AB\Rightarrow VC\perp (ABM)\Rightarrow VC\perp MN\Rightarrow m(MCN)=90\textdegree\Rightarrow \) \( \bigtriangleup{MNC} \)dreptunghic \( \Rightarrow \) cateta\( MN< \) ipotenuza \( CN \).