$\left. \begin{matrix} AB=AC\Rightarrow \hat{B}=\hat{C} \\ BD=BC\Rightarrow {{{\hat{D}}}_{1}}=\hat{C} \\ \end{matrix} \right\}\Rightarrow \left. \begin{matrix} \hat{B}={{{\hat{D}}}_{1}} \\ \hat{C}=\hat{C} \\ \end{matrix} \right\}$
$\Rightarrow A\overset{\Delta }{\mathop{B}}\,C\sim B\overset{\Delta }{\mathop{CD}}\,$
$\Rightarrow \frac{AC}{BC}=\frac{BC}{CD}$
$\Rightarrow \frac{9}{BC}=\frac{BC}{4}\Rightarrow B{{C}^{2}}=36\Rightarrow BC=6\Rightarrow BD=6$
$\Rightarrow $ محیط $B\overset{\Delta }{\mathop{CD}}\,=16$
