Corollary: 3.16: Line at Right Angles to Diameter of Circle At its Ends Touches the Circle
(related to Proposition: 3.16: Line at Right Angles to Diameter of Circle At its Ends Touches the Circle)
(Corollary to Proposition 16 from Book 3 of Euclid's “Elements”)
So, from this, (it is) manifest that a (straight line) drawn at right angles to the diameter of a circle, from its extremity, touches the circle [and that the straight line touches the circle at a single point, in as much as it was also shown that a (straight line) meeting (the circle) at two (points) falls inside it [Prop. 3.2] (Which is) the very thing it was required to show.
A straight line perpendicular to a diameter of a circle and going through one of its ends is obviously a tangent, i.e. it has only one point in common with the circle.
Table of Contents
Proofs: 1 2 3 4
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"