Vertical diameter theorem is a theorem in mathematical plane geometry (circle). Its popular expression is: the diameter perpendicular to the chord bisects the chord and bisects the two arcs opposite to the chord. The mathematical expression is as follows: if the diameter DC is perpendicular to the chord AB, AE=EB, the arc AD is equal to the arc BD (including the upper arc and the lower arc), and the semicircle CAD= semicircle c BD.

The diameter perpendicular to the chord bisects the chord and bisects the two arcs opposite the chord.

As long as a straight line has any two of the following five conditions, the other three conclusions can be deduced. It is called knowing two makes three (knowing two pushes three).

The best arc to bisect the chord.

The lower arc bisecting the chord (the first two together are: the two arcs bisecting the chord)

Bisecting chord

Perpendicular to the chord

Pass through the center (or diameter)

Inference 1: The diameter (non-diameter) of the bisecting chord is perpendicular to this chord and bisects the two arcs opposite to this chord.

Inference 2: The diameter of the arc bisecting a chord bisects this chord vertically and bisects another arc opposite this chord.

Inference 3: In the same circle or equal circle, the arcs sandwiched by two parallel chords are equal.

I hope it can help you solve the problem.