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Proof of mathematical circle in grade three.
Proof: even BC, OE,

△OEF,OE=OF=√2,EF=2。

∵(√2)? +(√2)? =2?

∴OE? +OF? =EF?

That is, △OEF is Rt△, ∠ EOF = 90.

∫ Point E is the midpoint of arc AC, and point F is the midpoint of arc AB.

∴ arc BC is: 90× 2 = 180.

BC is the diameter of this circle.

∴∠CAB=90

Namely: AC⊥AB