解答下该题---如图所示的四棱锥 P-ABCD 中, PA ⊥ 平面 ABCD, BC || AD, AB ⊥ AD. (1) 证明: 平面 PAB ⊥ 平面 PAD; (2) 若 PA = AB = √2, AD = √3 + 1, BC = 2, P,B,C,D 在同一个球面上, 设该球面的球心为 O. (i) 证明: O 在平面 ABCD 上; (ii) 求直线 AC 与直线 PO 所成角的余弦值. Chart/Diagram Description: Type: 3D geometric figure of a quadrangular pyramid. Main Elements: Vertices: Labeled P, A, B, C, D. Edges: PA, PB, PC, PD, AB, BC, CD, DA. PA, AB, and AD are shown as dashed lines, likely representing the orientation or hidden parts relative to the base plane. PB, PC, PD, BC, CD are shown as solid lines. Base: Quadrilateral ABCD is the base. Apex: P is the apex. Relative Position: P is positioned above the base ABCD. PA is the vertical edge from P to vertex A of the base. Note: The question specifies that PA is perpendicular to the plane ABCD, BC is parallel to AD, and AB is perpendicular to AD. The diagram visually represents this setup in perspective.