\( A B \) - перпендикуляр к плоскости \( \alpha \cdot A D \) и \( A C \) - наклонные к \( \alpha, B D=6, A D=10, A C=16 \). Найдите \( \angle A C B \).

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

Dado un cilindro con un radio de 4 cm, ¿cuál debe ser la altura para que el volumen sea \( 64\pi \) cm³?

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

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

e) La somma e la differenza delle diagonali di un rombo misurano 126 cm e 18 cm . Calcola la misura del raggio della circonferenza inscritta nel rombo.