Page 1 of 1
Suma vectoriala nula
Posted: Mon Dec 28, 2009 4:38 pm
by Claudiu Mindrila
Fie \( \triangle{ABC} \) iar \( H \) ortocentrul sau. Sa se arate ca
\( \tan A\cdot\vec{HA}+\tan B\cdot\vec{HB}+\tan C\cdot\vec{HC}=\vec{0} \)
Posted: Mon Dec 28, 2009 8:03 pm
by DrAGos Calinescu
In general, pentru orice punct \( O \) din plan exista relatia
\( \vec{OH}=\frac{\tan A\cdot\vec{OA}+\tan B\cdot\vec{OB}+\tan C\cdot\vec{OC}}{\tan A+\tan B+\tan C} \)
Re: Suma = \vec{0}
Posted: Mon Dec 28, 2009 8:25 pm
by Marius Mainea
Claudiu Mindrila wrote:
\( \tan A\cdot\vec{HA}+\tan B\cdot\vec{HB}+\tan C\cdot\vec{HC}=\vec{0} \)
Relatia se reduce la
\( \left{\begin{array}{cc}\tan B\cdot\vec{A^{\prime}B}+\tan C\cdot\vec{A^{\prime}C}=\vec{0}\\\tan A\cdot\vec{HA}+(\tan B+\tan C)\vec{HA^{\prime}}=\vec{0}\end{array} \)