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Mathematical problems of brain
Solution:

( 1)≈∠AOC =( 1/3)∠BOC

∴∠BOC=3∠AOC

∵∠AOC+∠BOC= 180

∴4∠AOC= 180

∠AOC = 45°

∫OC is the bisector of∝∠ ∝∠AOD,

∴ ∠COD=∠AOC=45

(2) From (1) ∠ COD = ∠ AOC = 45.

∠ AOD =∠ COD +∠ AOC = 90。

∴OD⊥AB