mateforum.ro Forum Index mateforum.ro

 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

Un loc geometric.

 
Post new topic   Reply to topic    mateforum.ro Forum Index -> Clasa a XI-a -> Geometrie analitica
View previous topic :: View next topic  
Author Message
Virgil Nicula
Euler


Joined: 28 Sep 2007
Posts: 672

PostPosted: Mon Mar 23, 2009 5:01 pm    Post subject: Un loc geometric. Reply with quote

In interiorul unui triunghi ABC se considera un punct mobil L pentru care definim

intersectiile E\in AC\cap BL si F\in AB\cap CL . Sa se determine locul geometric al

punctelor L cu proprietatea ca patrulaterul corespunzator AELF este circumscriptibil.
Back to top
View user's profile Send private message
mihai miculita
Pitagora


Joined: 12 Nov 2007
Posts: 94
Location: Oradea, Romania

PostPosted: Fri Mar 27, 2009 7:24 pm    Post subject: Reply with quote

\mbox{AELF-circumscriptibil}\Leftrightarrow |AB|+|LC|=|AC|+|BL|\Leftrightarrow |LC|-|BL|=|AC|-|AB|\Rightarrow\\
 \Rightarrow \mbox{punctul L se gaseste pe o hiperbola avand focarele in punctele B si C;}\dots\\
Demonstratia relatiei:  |AB|+|LC|=|AC|+|BL|.
\mbox{Notand cu } a,b,c \mbox{ si cu }l \mbox{ lungimile tangentelor duse din punctele A, B, C si respectiv L,}\\ 
\mbox{ la cercul inscris in patrulaterul AELF, avem: } |AB|+|LC|=(a+b)+(c-l)=(a+c)+(b-l)=|AC|+|BL|.
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    mateforum.ro Forum Index -> Clasa a XI-a -> Geometrie analitica All times are GMT + 2 Hours
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum



Powered by phpBB © 2001, 2005 phpBB Group