Prove:

Because OE shares ∠AOC, OF shares ∠BOC, ∠AOE=∠EOC=∠EOB+∠BOF+∠FOC,

Because ∠AOB=90 degrees, ∠AOE+∠EOB=90 degrees.

∠EOB+∠EOB+∠ Boff +∠FOC=90 degrees,

Because ∠BOF=∠FOC.

So, 2(≈BOF+≈BOF)= 90 degrees,

So ∠EOF=45 degrees.