Proposition: 3.19: Right Angle to Tangent of Circle Goes Through Center
(Proposition 19 from Book 3 of Euclid's “Elements”)
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.
Modern Formulation
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.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1
Thank you to the contributors under CC BYSA 4.0!
 Github:

 nonGithub:
 @Fitzpatrick
References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016