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A math test (20 13 Longdong area, Heilongjiang province)
2) Conclusion of Figure 2: af-BF = 2oe,

Figure 3 Conclusion: AF-BF = 2oe.

Prove to Figure 2 that point B is the extension line of BG⊥OE and OE at point G,

The quadrilateral BGEF is a rectangle,

∴EF=BG,BF=GE,

In the square ABCD, OA=OB, ∠ AOB = 90,

∵BG⊥OE,

∴∠OBG+∠BOE=90,

∠∠AOE+∠BOE = 90,

∴∠AOE=∠OBG,

At △AOE and △OBG,

∴△AOE≌△OBG(AAS),

∴OG=AE,OE=BG,

∵af﹣ef=ae,ef=bg=oe,ae=og=oe+ge=oe+bf,

∴AF﹣OE=OE+BF,

∴af﹣bf=2oe;

Fig. 3 proves to be consistent with fig. 2.