Diameter through chord midpoint ⊥ chord

Dependencies: Perpendicular bisector ⇔ equidistant from endpoints, Perpendicular bisector test.

Statement

In $\odot O$, let $AB$ be a chord (not passing through the center) and let $M$ be the midpoint of $AB$. Extend the line $OM$ into a diameter through the center $NS$. Then

In other words, the two conditions "through the center" and "bisects the chord" together $\Rightarrow$ "perpendicular to the chord" comes for free, no extra hypothesis required.