How is constructing a perpendicular bisector similar to constructing an angle bisector? how is it different?

Similarities between angle bisector and perpendicular bisector:
Perpendicular bisector bisects a line segment into two equal parts at 90°.
Angle bisector bisects an creating two congruent angles
they both bisect into equal parts

Construction of an angle bisector starts by defining a segment that is a chord of a circle with the given angle as the central angle. From there, the constructions proceed in the same way, as the perpendicular bisector of the chord bisects the central angle.

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