In a circle, if any straight line through the center cuts in half any straight line not through the center then it also cuts it at right angles. And (conversely) if it cuts it at right angles then it also cuts it in half. * Let $ABC$ be a circle, and, within it, let some straight line through the center, $CD$, cut in half some straight line not through the center, $AB$, at the point $F$. * I say that ($CD$) also cuts ($AB$) at right angles.
Let $AB$ be a chord, which does not go through the center $E$ of a given circle and let $CD$ be its diameter, i.e. it goes through the center $E.$
Then $CD$ bisects $AB$ if and only if $CD\perp AB,$ i.e. both are perpendicular.
Proofs: 1
