2012 AMC 12A 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\qquad\textbf{(B)}\ 5+\sqrt{26}+3\sqrt{3}\qquad\textbf{(C)}\ 3\sqrt{26}\qquad\textbf{(D)}\ \frac{2}{3}\sqrt{546}\qquad\textbf{(E)}\ 9\sqrt{3}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.