作图解答这道题---**Extraction Content:** **Question Stem:** 如图，正方形ABCD边长为4，在RT△EFG组，∠FEG=90°，EF=FG=2√2，D是斜边FG中点，连接BE，P为BE中点，连接PC，求：PC的最大和最小值？ **Other Relevant Text:** (Watermark) @阿古数学 求PC的最大最小值？ **Mathematical Formulas/Equations/Data:** 正方形ABCD边长为4 RT△EFG (Right-angled triangle EFG) ∠FEG=90° EF=FG=2√2 D是斜边FG中点 P为BE中点 **Chart/Diagram Description:** * **Type:** Geometric figure. * **Main Elements:** * **Shapes:** * Square ABCD. * Right-angled triangle EFG. * **Points:** A, B, C, D (vertices of the square), E, F, G (vertices of the triangle), D (also the midpoint of FG), P (midpoint of BE). * **Lines:** * Sides of the square: AB, BC, CD, DA. * Sides of the triangle: EF, EG, FG. * Line segment BE. * Line segment PC. * **Angles:** ∠FEG is indicated as a right angle (90°). * **Labels:** All points are labeled A, B, C, D, E, F, G, P. * **Relative Position and Direction:** * Square ABCD is shown. * Triangle EFG is shown; point E is positioned inside or near the square. * Vertex D of the square is located on the line segment FG and is explicitly stated to be the midpoint of the hypotenuse FG. * Line segment BE connects vertex B of the square to vertex E of the triangle. * Point P is located on line segment BE, at its midpoint. * Line segment PC connects point P to vertex C of the square. * **Annotations:** The watermark "@阿古数学" is present.