讲解一下这道题目---**Textual Information:** **Question Stem:** In the quadrilateral pyramid P-ABCD shown in the figure, PA is perpendicular to plane ABCD (PA ⊥ plane ABCD), BC is parallel to AD (BC // AD), and AB is perpendicular to AD (AB ⊥ AD). **(1)** Prove: Plane PAB is perpendicular to Plane PAD (Plane PAB ⊥ Plane PAD). **(2)** If PA = AB = √2, AD = √3 + 1, BC = 2, and points P, B, C, D are on the same sphere, let the center of the sphere be O. **(i)** Prove: O is on plane ABCD. **(ii)** Find the cosine value of the angle between line AC and line PO. --- **Chart/Diagram Description:** * **Type:** A 3D geometric figure, specifically a quadrilateral pyramid. * **Main Elements:** * **Vertices:** Labeled points P, A, B, C, D. P is the apex, and A, B, C, D are the vertices of the base. * **Base:** A quadrilateral ABCD. Given the conditions, the base ABCD is a right trapezoid with AD parallel to BC, and AB perpendicular to AD. * **Edges:** * **Solid lines (visible edges):** PB, PC, PD, BC, CD. * **Dashed lines (hidden edges):** PA (the height of the pyramid), AB, AD (edges of the base). * **Relative Position:** The apex P is positioned vertically above vertex A of the base. The base ABCD lies in a horizontal plane. * **Labels and Annotations:** All vertices (P, A, B, C, D) are clearly labeled.