AD is perpendicular to DC in math problems of grade three in Shandong province; AB is perpendicular to BC; EF is perpendicular to BD; AG is parallel to EF and parallel to HC; E is the midpoint of communication; BD = 8； AC = 10； Looking for AG I think this question should be unqualified.

Because the vertices ABCD of ABC and ADC are on a circle with E as the center and AC as the diameter.

In the right triangle DFE, EF=3.

As long as the length of the chord BD of the circle E is 8, BD can "slide" on the circle, so the shortest length of AG is 0 and the longest is 2.

The length of CH or AG should be given again.