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Mathematical counterexamples, such as
1. let EG⊥OA be in g,

∫EF∨OB,

∴∠OEF=∠COE= 15,

∫∠AOE = 15,

∴∠EFG= 15 + 15 =30,

∫EG = CE = 1 (the distance from the bisector of the angle to both sides of the angle is equal),

∴ ef = 2× 1 = 2 (the right angle side facing 30 is half of the hypotenuse).

2. Wrong

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