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Some math problems. Write simple ideas and processes.
Proof: FD = FO, ∠DFE=∠EFO, FT=FT,

∴△OTF≌△DTF,

∴∠TOF=∠TDF=∠ADE,

AD = OG,∠A=∠TGO=90,

∴Rt△AED≌Rt△GTO,

∴ED=OT,

OA = DG,AE=TG,

∴DT=EO,

∴ED=DT=OT=OE,

The quadrangle OEDT is a diamond.

Solution: Using Figure 2'Rt△DBC, we can get: (10-x)2= 102-62.

The solution is x=2 or x= 18 (irrelevant, omitted).

Using the results of Figure 2 and (1), x=6,

So 2≤x≤6,

According to the meaning of the question: x2+(6-L 4 )2=(L 4 )2,

So L= 12+x2 3 (2≤X≤6),

Since the function value L increases with the increase of X on the right side of the coordinate axis (L axis), when x=6, L takes the maximum value.

L max = 12+62 3 =24,

A: When X is 6, the circumference L of the diamond OEDT is the largest, and the maximum circumference L is 24.