F) Considérons le plan ou l'espace muni d'un repère. Déterminez le milieu des segments \( [A B] \) si \( \begin{array}{ll}\text { 1) } A(-1 ; 1) \text { et } B(2 ; 3) & \text { 2) } A=O \text { et } B=(1 ;-4) \\ \text { 3) } A(1 ;-2 ; 4) \text { et } B(-1 ; 2 ;-1) & \text { 4) } A(3 ;-7 ; 2) \text { et } B(-4 ; 6 ;-1)\end{array} \)

The geometrical centre of square ABCD is the origin and its side length is \( 2 \sqrt{3} \) , then the equation of the circle that touches its sides is \( \begin{array}{ll}\text { (a) } x^{2}+y^{2}=3 & \text { (b) } x^{2}+y^{2}=12 \\ \text { (c) } x^{2}+y^{2}=6 & \text { (d) }(x-\sqrt{3})^{2}+(y-\sqrt{3})^{2}=3\end{array} \)

If the straight line \( y=m x \) touches the circle \( (x-2)^{2}+(y-6)^{2}=4 \), then \( m=\ldots \ldots \) \( \begin{array}{llll}\text { (a) } \frac{1}{3} & \text { (b) } \frac{2}{3} & \text { (c) } \frac{-4}{3} & \text { (d) } \frac{4}{3}\end{array} \)

A cuboid has a total surface area of \( 94 \mathrm{~cm}^{2} \). If its length is 5 cm and breadth is 3 cm , find its height.

The edge of a cube is doubled. By what factor will its surface area and volume increase?

Given: \( \angle A \cong \angle E \) \( A B \cong E D, B C \cong D C, A C \cong E C \) Prove: \( \triangle A C B \cong A E C D \) Statements 1. 2. \( A B \cong E D, B C \cong B C, A C \cong E C \) 3. \( \angle A D \angle A C B \cong \angle E C D \) 4. \( \angle A B C \cong \angle E D C \) S. \( \angle A \) angles