AMC 12 2012a Problem 18

Triangle $ABC$ has $AB=27$, $BC=25$, and $CA=26$. Let $I$ denote the intersection of the internal angle bisectors of $\triangle ABC$. What is $BI$?

\textbf{(A)}\ 15 \textbf{(B)}\ 5+\sqrt{26}+3\sqrt{3} \textbf{(C)}\ 3\sqrt{26} \textbf{(D)}\ \frac{2}{3}\sqrt{546} \textbf{(E)}\ 9\sqrt{3}