Proposition: 3.18: Radius at Right Angle to Tangent
(Proposition 18 from Book 3 of Euclid's “Elements”)
If some straight line touches a circle, and some (other) straight line is joined from the center (of the circle) to the point of contact, then the (straight line) so joined will be perpendicular to the tangent.
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Modern Formulation
If a tangent and a radius of a given circle intersect, then they are perpendicular.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4 5 6
Thank you to the contributors under CC BY-SA 4.0!
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References
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016