请解答这个数学题目---**Problem Description:** In △ABC, ∠BAC=90°, AB=AC, point P is a point on the extension of BA. Connect PC, with P as the center, rotate line segment PC clockwise by 90° to obtain line segment PD, connect BD. **(1) Complete the figure according to the problem description;** **(2) Prove: ∠ACP = ∠DPB;** **(3) Express the quantitative relationship between line segments BC, BP, BD using an equation, and prove it.** **Geometric Figure Description:** * **Type:** Geometric figure showing a triangle and a line segment extending from a vertex. * **Elements:** * A triangle labeled ABC. * Vertex A is marked with a right angle symbol (indicating ∠BAC = 90°). * Point P is located on a line extending from vertex A through vertex B. * Points B, A, and P are collinear in that order on a straight line. * Line segments AB, AC, BC, and PC are shown. * The labels A, B, C, and P are clearly marked at their respective points. * **Relative Position:** * A is a vertex of the triangle, and also lies on the line segment BP. * B is a vertex of the triangle and lies on the line segment AP. * C is a vertex of the triangle. * P lies on the extension of BA, beyond A (as depicted in the figure and stated in the text as extension of BA, implying the order B-A-P). The text says P is on the extension of BA, which means A is between B and P if extending BA from B towards A. However, the figure shows B-A-P. Let's re-read carefully: "点 P 为 BA 的延长线上一点". This means extending the line segment BA beyond A. So the order is B -> A -> P. The figure is consistent with this. * PC is a line segment connecting points P and C. * The figure provided shows the initial setup before the rotation described in the problem. It does not show point D or line segment BD which need to be added as per instruction (1).