L'area di un rettangolo è \( 512 \mathrm{~cm}^{2} \) e la base è il doppio dell'altezza. Calcola la misura del peri- metro.

Cos'è un cerchio?

3) The exterior bisector of the vertex angle of an isosceles triangle \( \cdots \cdots . . . \). the base. \( \begin{array}{ll}\text { (a) bisects } & \text { (b) perpendicular to } \\ \text { (c) intersect } & \text { (d) parallel }\end{array} \)

6. \( A D, B E \) and \( C F \) are the three altitudes of \( \triangle A B C \). Show that \( \begin{array}{ll}\text { (i) Perimeter of triangle } A B C>2 A D & \text { (ii) Perimeter of triangle } A B C>2 B E \\ \text { (iii) Perimeter of triangle } A B C>2 C F & \text { (Perimeter of triangle } A B C)>2(A D+B E+C F)\end{array} \)

\( A B C \) est un triangle et \( I \) milieu de \( [B C] \). 1) Soit \( \operatorname{Ebar}\{(A, 1) ;(B, 2) \),\( \} et F b a r\{(B, 2) ;,(C, 1)\} \). a) Montrer que: \( \overrightarrow{A E}=\frac{2}{3} \overrightarrow{A B} \). b) Montrer que: \( \overrightarrow{B F}=\frac{1}{3} \overrightarrow{B C} \) c) Construire les points \( I, E \) et \( F \). 2) Soit \( G b a r\{(A, 1) ;(B, 2) ;,(C, 1)\} \). a) Montrer que \( \operatorname{Gbar}\{(A, 1) ;(F, 3) \),\( \} . \) b) Montrer que \( G \in(E C) \). c) Montrer que \( G \in(I B) \) et construire \( G \). 3) Determiner l'ensemble des points \( M \) du plan qui verifient chacune des équations suivantes: a) \( \|\overrightarrow{M A}+2 \overrightarrow{M B}+\overrightarrow{M C}\|=8 \) b) \( \|\overrightarrow{M A}+2 \overrightarrow{M B}\|=\|\overrightarrow{M C}+2 \overrightarrow{M B}\| \)

In the opposite figure : \( \frac{\mathrm{BE}}{\mathrm{BC}}= \) \( \begin{array}{ll}\text { (a) } \frac{1}{2} & \text { (b) } 2 \\ \text { (c) } \frac{1}{3} & \text { (d) } 3\end{array} \)