There is a question (20 13 new textbook): seventh-grade mathematics learning in Shandong Education Press and you! ! ! ! ! ! ! ! ! ! ! ! !

AB=AG= 10cm, let BE=GE=x, then ce = BC-be = 6-x.

According to Pythagorean theorem in RT△GCE, there are:

GE^2=CE^2+CG^2

cg^2=ge^2-ce^2=x^2-(6-x)^2= 12x-36

CG=√( 12x-36)

So: DG = DC-CG = AB-CG =10-√ (12x-36).

According to Pythagorean Theorem, RT△ADG includes:

AG^2=DG^2+AD^2

10^2=[ 10-√( 12x-36)]^2+6^2

So: 10-√( 12x-36)=8.

So: √( 12x-36)=2.

So: 12x-36=4.

Solution: x=BE=8/3cm.