9. ABC is a triangle in which \( m \overline{\mathrm{BC}}=m \overline{\mathrm{CA}}=2 \mathrm{~m} \overline{\mathrm{AB}} \). Internal bisector of \( \angle A \) meets \( \overline{\mathrm{BC}} \) at D and \( \overline{\mathrm{DE}} \) is drawn parallel to \( \overline{\mathrm{CA}} \) meeting \( \overline{\mathrm{AB}} \) at E . Find \( m \overline{\mathrm{DE}}: \mathrm{m} \overline{\mathrm{AB}} \).

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.

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

[b] If \( b \) is the middle proportional between \( a \) and \( c \) , then prove that : \( \frac{a-b}{a-c}=\frac{b}{b+c} \)

the area of \( \triangle A B C=12 \mathrm{~cm}^{2} \), then \( \left(b^{2}+c^{2}-a^{2}\right) \tan A=\cdots \) 12 (b) 24