Let `A B C D` be a rectangle and `P` be any point in its plane. Show that `A P^2+P C^2=P B^2+P D^2dot`

Explanation

To prove that \( AP^2 + PC^2 = PB^2 + PD^2 \) for a rectangle \( ABCD \) and any point \( P \) in its plane, we can follow these steps:

### Step 1: Define the Coordinates
Let the rectangle \( ABCD \) be defined in the Cartesian plane as follows:
- \( A(0, 0) \)
- \( B(a, 0) \)
- \( C(a, b) \)
- \( D(0, b) \)
...