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Perpendicular Bisector 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.