The vertical diameter theorem is a theorem in mathematical 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, if the diameter DC is perpendicular to the chord AB, AE=EB, arc AD = arc BD (including upper arc and lower arc), semicircle c AD = 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.

1, the optimal arc bisecting the chord;

2. bisect the lower arc opposite the chord (the first two together are: bisect the two arcs opposite the chord);

3. bisect the chord (not the diameter);

4, perpendicular to the chord;

5. Pass through the center of the circle.

Extended data:

1, bisecting the diameter of the chord perpendicular to the chord (not the diameter) and bisecting the two arcs opposite to the chord;

2. The arcs sandwiched by two bisecting chords of a circle are equal;

3. In the same circle or the same circle, if the sum of one set of quantities in two central angles, two arcs, two chords or the distance between two chords is equal, the corresponding other set of quantities are equal respectively;

4. Two tangents leading to the circle from a point outside the circle have the same tangent length, and the connecting line between the center of the circle and this point bisects the included angle of the two tangents.