Given that D is the incenter of the triangle, then BD is congruent to DG and DE.
Considering that triangle DGF is a right triangle, we can use the Pythagorean theorem, as follows:
[tex]\begin{gathered} DF^2=DG^2+GF^2 \\ 13^2=DG^2+12^2 \\ 169-144=DG^2 \\ \sqrt[]{25}=DG \\ 5=DG \end{gathered}[/tex]
Then, the measure of BD is 5 units
