The vertical diameter theorem is that the perpendicular bisects the chord with the diameter of the chord and bisects the two arcs opposite to the chord.

Inference 1: bisect the diameter (not the diameter) of the chord perpendicular to this chord and bisect the two arcs opposite to this chord.

Inference 2: The perpendicular line of a chord passes through the center of the circle and bisects the arc opposite to this chord.

Inference 3: The diameter of the arc bisecting a chord bisects this chord vertically and bisects another arc opposite this chord.

Inference 4: In the same circle or equal circle, the arcs sandwiched by two parallel chords are equal.