iran-konkur 2023 Q32

iran-konkur · Other · konkur-riazi_1402_general Sine and Cosine Rules Multi-step composite figure problem
32. In the figure below, if $\widehat{DAC} = 3\widehat{BAD}$, what is the length of side $AC$?
[Figure: Triangle with vertices $A$, $B$, $C$, point $D$ on $BC$ with $BD = 4$, $AB = 8$, $AD = 6$]
  • [(1)] $19/2$
  • [(2)] $16/8$
  • [(3)] $18/6$
  • [(4)] $15/4$
\textbf{32.} In the figure below, if $\widehat{DAC} = 3\widehat{BAD}$, what is the length of side $AC$?

\textit{[Figure: Triangle with vertices $A$, $B$, $C$, point $D$ on $BC$ with $BD = 4$, $AB = 8$, $AD = 6$]}

\begin{itemize}
    \item[(1)] $19/2$
    \item[(2)] $16/8$
    \item[(3)] $18/6$
    \item[(4)] $15/4$
\end{itemize}