What is a circle?

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

Cos'è un cerchio?

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.

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

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