iran-konkur 2023 Q26

iran-konkur · Other · konkur-riazi_1402_general Straight Lines & Coordinate Geometry Triangle Properties and Special Points
26. In the figure below, $\hat{ABF} = C\hat{A}E = B\hat{C}D$, $DF = 2.5$, and $EF = 3$. What is the length of $AB$?
[Figure: Triangle ABC with point D on side AB, point E on side BC, and point F inside the triangle, with lines drawn from vertices through F]
  • [(1)] $8.6$
  • [(2)] $7.5$
  • [(3)] $10.5$
  • [(4)] $9.6$
\textbf{26.} In the figure below, $\hat{ABF} = C\hat{A}E = B\hat{C}D$, $DF = 2.5$, and $EF = 3$. What is the length of $AB$?

\textit{[Figure: Triangle ABC with point D on side AB, point E on side BC, and point F inside the triangle, with lines drawn from vertices through F]}

\begin{itemize}
    \item[(1)] $8.6$
    \item[(2)] $7.5$
    \item[(3)] $10.5$
    \item[(4)] $9.6$
\end{itemize}