If some straight line touches a circle, and a straight line is drawn from the point of contact, at right-[angles to the tangent, then the center (of the circle) will be on the (straight line) so drawn. * For let some straight line $DE$ touch the circle $ABC$ at point $C$. * And let $CA$ have been drawn from $C$, at right angles to $DE$ [Prop. 1.11]. * I say that the center of the circle is on $AC$.
If a straight line ($AC$) is perpendicular to a tangent ($DE$) and goes through the point ($C$) at which the tangent touches the circle, then the straight line also goes through the center of the circle.
Proofs: 1
Proofs: 1