Inegalitate in tetraedru 1

Marius Mainea · Post by **Marius Mainea** » Sun Jan 18, 2009 6:41 pm

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 \( MN< CN \)

Marius Mainea · Post by **Marius Mainea** » Wed Dec 16, 2009 5:41 pm

Indicatie: \( VC\perp(ABM) \)

Andi Brojbeanu · Post by **Andi Brojbeanu** » Wed Jan 13, 2010 6:19 pm

\( BM\perp VC\Rightarrow VC\perp BM \).
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 \( CN \).