Proposition: 3.11: Line Joining Centers of Two Circles Touching Internally
(Proposition 11 from Book 3 of Euclid's “Elements”)
If two circles touch one another internally, and their centers are found, then the straight line joining their centers, being produced, will fall upon the point of union of the circles.
* For let two circles, $ABC$ and $ADE$, touch one another internally at point $A$, and let the center $F$ of circle $ABC$ have been found [Prop. 3.1], and (the center) $G$ of (circle) $ADE$ [Prop. 3.1].
* I say that the straight line joining $G$ to $F$, being produced, will fall on $A$.
If two circles touch one another internally at a point $A$, then the straight line going through their centers goes also through $A$.
Table of Contents
Proofs: 1 2
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