9. $( a * b ) \quad \mathrm { lcm } = k m ; g c d = m ; a = k m ; b = k n ; c = k p$

$$\begin{array} { l l } 
( a * b ) = \frac { k m n } { k } = m n ; b * c = \frac { k n p } { k } = n p & \\
( a * b ) * c = k m n p / 1 = k m n p & a = k m \quad i = k p \\
( a * ( b * c ) ) = k m n p / 1 = k m n p & a * i = k m p / k = m p \neq a
\end{array}$$

\begin{enumerate}
  \setcounter{enumi}{9}
  \item 'any two similar figures have an isomerism and homethette velation which takes are figure to the other'\\
a) have segment $A B ( A \neq B )$ and $C D ( C \not \equiv D )$. Have point $P \in A B$ with $P A / A B = \lambda \in [ 0,1 ]$; assocrate to it the point SECD with SC/CD $= \lambda$\\
b) have cincle $\gamma$ (of the centre $m$ and radius $r > 0$ ) and $\Gamma$ (of centre $m$ and radius $R > 0$ ). Have point $P + \gamma$ making angle $\theta \in [ 0,2 \pi )$ with the horizontal; asscerate to it point $Q \in T ^ { \prime }$ making an angle $\theta$ with the horizontal
\end{enumerate}