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. Mathematically, as shown in the following figure, if the diameter DC is perpendicular to the chord AB, AE equals EB, arc AD equals arc BD (including upper arc and lower arc), and semicircle c AD equals semicircle c BD.

Theorem definition

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)