If a number of circles pass through the end points P and Q of a line segment PQ, then Prove that their centres lie on the perpendicular bisector of PQ.

Explanation

To prove that the centers of all circles passing through the endpoints P and Q of a line segment PQ lie on the perpendicular bisector of PQ, we can follow these steps:

### Step 1: Define the Points
Let the points P and Q be defined in a Cartesian coordinate system. Assume:
- P = (x1, y1)
- Q = (x2, y2)

### Step 2: Find the Midpoint of PQ
...