iran-konkur 2021 Q152

iran-konkur · Other · konkur-riazi_1400_specialized Circles Tangent Lines and Tangent Lengths
152. In the figure below, line segment $AC$ is tangent to the circle. If $\dfrac{AC}{BC} = \sqrt{3}$, then what is $\dfrac{DB}{BC}$?
[Figure: Circle with points A, B, C, D, where AC is tangent to the circle at C]
  • [(1)] $\sqrt{2}$
  • [(2)] $\sqrt{3}$
  • [(3)] $2$
  • [(4)] $3$

\textbf{152.} In the figure below, line segment $AC$ is tangent to the circle. If $\dfrac{AC}{BC} = \sqrt{3}$, then what is $\dfrac{DB}{BC}$?

\textit{[Figure: Circle with points A, B, C, D, where AC is tangent to the circle at C]}

\begin{itemize}
    \item[(1)] $\sqrt{2}$
    \item[(2)] $\sqrt{3}$
    \item[(3)] $2$
    \item[(4)] $3$
\end{itemize}

\vspace{0.5cm}