X EXERCICE 15 \( A B C \) est un triangle. 1. Construire le point \( D \) tel que \( \overrightarrow{A D}=\overrightarrow{A B}-\overrightarrow{A C} \). Que peut-on dire du quadrilatère \( A D B C \) 2. Construire le point \( M \) tel que \( \overrightarrow{B M}=\overrightarrow{B C}-\overrightarrow{C A} \).

В треугольнике \( N B T \) проведена медиана \( B S \). ериметр треугольника \( N B S \) равен 22 см, периметр реугольника \( S B T \) равен 18 cm . Найдите периметр реугольника \( N B T \), если \( B S=8 \mathrm{~cm} \).

What are their sizes? One of the angles formed when two lines intersect is \( 127^{\circ} \). What are the sizes of the other three angles?

\( \begin{array}{lr}24 \text { Due triangoli } A B C \text { e } A^{\prime} B^{\prime} C^{\prime} \text { sono tali che } A B \cong A^{\prime} B^{\prime}, \\ B C \cong B^{\prime} C^{\prime} \text { e uno degli angoli esterni di vertice } B \text { è con- } \\ \text { gruente a uno degli angoli esterni di vertice } B^{\prime} \text {. Dimo- } & \text { cui } \\ \text { stra che i due triangoli sono congruenti. }\end{array} \)

5. Найти площадь фигуры, огғ \( y=-x^{2}-4 x \) и \( у=4+x \)

Two circles, \( c_{1} \) and \( c_{2} \), touch internally. The equations of the circles are: \[ c_{1}:(x+1)^{2}+(y-3)^{2}=49 \] \[ c_{2}: x^{2}+y^{2}-6 x-12 y+k=0 \] Work out the two possible values of \( k \), where \( k \in \mathbb{Z} \).