# Perpendicular Bisector Explanation

- Author:
- Caribou Contests

- Topic:
- Geometry, Line Segment

## Explanation

Let the point of intersection of AB and CD be M. Because of mirror symmetry with respect to line AB ∠AMC = ∠AMD and because their sum is 180°, each must be 90°. To construct a perpendicular line the two circles do not have to have the same radius. For M to be the midpoint of AB we need symmetry with respect to the line CD. This means both circles need the same radius but that radius can be different from AB.