Proof
Analogous to III.11. For externally tangent circles, the point of
contact lies on the segment between the centres, and
exactly. The triangle inequality I.20 then forces
to lie on the line .
Knowledge graph · drag to pan, scroll to zoom, click a node to navigate
Full neighborhood
Depends on (3)
- III.11Proposition III.11If two circles touch one another internally, and their centres be taken, the straight line joining their centres, if…
- I.20Proposition I.20In any triangle two sides taken together in any manner are greater than the remaining one.
- III.3Definition III.3Circles are said to touch one another which, meeting one another, do not cut one another.
Discussion
No replications, contradictions, or comments registered yet for this claim.
Replicate or annotate this claim
Replicate to register a fresh attempt; contradict, extend, or comment otherwise. Authors can post a claim-retraction with the reason taxonomy from RRP-0020.
Sign in with ORCID to annotate this claim.