(1) Because ∠ ADB = 90 (the circumferential angle on the right angle is equal to the right angle), ∴∠BDC = 90°.

In △ABC and △BDC, ∠DBC=∠BAC (known), ∠C=∠C, ∴∠ ABC = ∠ BDC = 90,

∴AB⊥BC, ∴BC is the tangent of ⊙ O.

(2) If the radius ⊙O is 2 and ∠ BAC = 30, find the area of the shaded part in the figure.

∵∠BAC = 30°, ∴∠BOD = 60° (the central angle is equal to twice the circular angle).

Sector OBD area = (2x2xπ)/(360/60) = 4π/6 = 2π/3.

△OBD area =2x√(4- 1)/2=√3

Shadow area = 2π/3-√ 3 ≈ 2.093-1.732 = 0.361.