The length of the two parallel sides of a right trapezoid are 6 cm and 8 cm, respectively top and bottom bases, and the altitude is 4 cm. The distance between the intersection of the two straight lines that contain the non-parallel legs and the midpoint of the major base is:
In the picture below, ABCD is a rectangle, $\,\overline{AB}\,=\,4\,$, $\,\overline{BC}\,=\,1\;$ and $\,\overline{DE}\,=\,\overline{EF}\,=\,\overline{FC}\;$. The length of $\,\overline{BG}\,$ is: