(1) When the coordinates of point A are (1,0), AB=AC=2-1, the coordinates of point C are (1,2-1) or (1,1-2 );

When the coordinates of point A are (-1, 0), AB=AC=2+1, the coordinates of point C are (-1, 2+1) or (-1,- 2-1);

(2) Straight line BC is tangent to ⊙O

Through point O, draw OM⊥BC at point M,

∴∠OBM =∠BOM=45°,

∴OM=OB?sin45°=1

∴Line BC is tangent to ⊙O;

(3) Pass Point A is drawn as AE⊥OB at point E

In Rt△OAE, AE2=OA2-OE2=1-x2,

In Rt△BAE, AB2=AE2+BE2 =(1-x2)+(2-x)2=3-22x

∴S=