iran-konkur 2023 Q30

iran-konkur · Other · konkur-riazi_1402_general Circles Tangent Lines and Tangent Lengths
30. In the figure below, two tangent lines are drawn from point $A$. What is the radius of the circle?
[Figure: Two tangent lines drawn from external point $A$ to a circle, with segments labeled 9, 8, 7 and point $B$, $C$ marked]
  • [(1)] $7/2\sqrt{2}$
  • [(2)] $4/8\sqrt{5}$
  • [(3)] $3/6\sqrt{2}$
  • [(4)] $2/4\sqrt{5}$
\textbf{30.} In the figure below, two tangent lines are drawn from point $A$. What is the radius of the circle?

\textit{[Figure: Two tangent lines drawn from external point $A$ to a circle, with segments labeled 9, 8, 7 and point $B$, $C$ marked]}

\begin{itemize}
    \item[(1)] $7/2\sqrt{2}$
    \item[(2)] $4/8\sqrt{5}$
    \item[(3)] $3/6\sqrt{2}$
    \item[(4)] $2/4\sqrt{5}$
\end{itemize}