\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}