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**Problem Number:** 24
**Problem Statement:**
As shown in Figure 1, in a planar rectangular coordinate system, the coordinates of points A and B are A (a, 0) and B (n, 0), and a, n satisfy |a+2| + √(5-n) = 0. Points A and B are simultaneously translated upwards by 4 units, then translated to the right by 3 units, respectively obtaining the corresponding points C and D. Connect AC, BD, CD.
**(1) Question:** Find the coordinates of points C, D, and the area of quadrilateral OBDC.
**(2) Question:** As shown in Figure 2, if point P is a moving point on line segment BD, connect PC, PO. When point P moves on BD (not coinciding with B, D), does the value of (∠DCP + ∠BOP) / ∠CPO change? Explain the reason.
**(3) Question:** In quadrilateral OBDC, does there exist a point P, connect PO, PB, PC, PD, such that Area(△PCD) = Area(△PBD); Area(△POB) = Area(△POC) = 1? If such a point exists, find the coordinates of point P. If it does not exist, explain the reason.
**Mathematical Formulas/Equations:**
|a+2| + √(5-n) = 0
Area(△PCD) = Area(△PBD)
Area(△POB) = 1
Area(△POC) = 1
**Charts/Diagrams:**
**Figure 1 (图1):**
* **Type:** Coordinate system diagram.
* **Main Elements:**
* Coordinate Axes: X-axis (labeled x), Y-axis (labeled y), Origin (labeled O).
* Points: A and B are on the x-axis. A is to the left of O. B is to the right of O. C and D are in the first quadrant. C is above A and to the right of A. D is above B and to the right of B.
* Lines: Straight line segment AC connects A and C. Straight line segment BD connects B and D. Straight line segment CD connects C and D. Straight line segment OB is the part of the x-axis from O to B. Straight line segment OC connects O and C.
* Shapes: Quadrilateral OBDC is formed by points O, B, D, C.
**Figure 2 (图2):**
* **Type:** Coordinate system diagram showing a moving point.
* **Main Elements:**
* Coordinate Axes: X-axis (labeled x), Y-axis (labeled y), Origin (labeled O).
* Points: A and B are on the x-axis. O is the origin. C and D are in the first quadrant. P is a point on the line segment BD.
* Lines: Straight line segment AC connects A and C. Straight line segment BD connects B and D. Straight line segment CD connects C and D. Straight line segment OB is the part of the x-axis from O to B. Straight line segment OC connects O and C. Straight line segment PC connects P and C. Straight line segment PO connects P and O.
* Shapes: Quadrilateral OBDC is formed by points O, B, D, C. Triangle PCD, Triangle PBD, Triangle POB, Triangle POC.