As shown in the figure, in the plane rectangular coordinate system, the straight line AB intersects the X axis and the Y axis at points A (4,0) and B (0,3) respectively. The coordinate of point C is (0, m), point C is point E CE⊥AB, and point D is the moving point of the positive semi-axis of X axis, which satisfies OD=2OC and connects DE and DE.

(1) Find the length of AE when m= 1.

(2) When 0

(3) Is there an m value that makes □DEFA a diamond? If it exists, write the value of m directly; If it does not exist, please explain why.

(This question is 14)

(1) solution: when m= 1, OC= 1, BC=2.

∴△BCE∽△BAO ∴ ∴

∴∴ ..........................4.

(2) Solution: When 0

When □ Germany and France are rectangular, then ED⊥x axis.

∴△ADE∽△AOB ∴ ∴

From the calculation of (1), we can know Ⅷ. ................................................................................................................................................

∴∴ ............................. 2 points.

When point m>2 and point D are on the right side of point A, then ∠ EDA < ∠EAO.

∴∠EDA can't be 90 years old, and ∴∴∴∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠.

(3) or ... 4 points.