26. (Chongqing, 20 12) As shown in the figure, in the right-angled trapezoidal ABCD, AD∨BC, ∠ B = 90, AD = 2°, BC = 6°, AB = 3. E is a point on the side of BC. Make a square BEFG with BE as the side, so that both the square BEFG and the trapezoidal ABCD are in BC.

(1) Find the length of BE when the vertex f of the square just falls on the diagonal AC;

(2) Translate the square B'EFG( 1) in question to the right along BC. Note that the square BEFC in translation is a square B'EFG, and stop translating when point E coincides with point C. Let the translation distance be t, and the side EF of the square B'EFG intersects with AC at point M to connect B'D, B'M and DM. Is there such a t that if △ exists, find the value of t; If it does not exist, please explain the reason;

(3) In the translation process of question (2), let the area of the overlapping part of square B'EFG and △ADC be S, please directly write the functional relationship between S and T and the range of independent variable T. 。

Inspection center: the judgment and nature of similar triangles; Pythagorean theorem; The nature of a square; Right trapezoid.

Solution: Solution: (1) As shown in Figure ①,

Let the side length of square BEFG be x,

Then BE=FG=BG=x,

AB = 3，BC=6，

∴AG=AB﹣BG=3﹣x，

∫GF∨BE，

∴△AGF∽△ABC，

∴AG/AB=GF/BC