Proposition: 3.09: Condition for Point to be Center of Circle
(Proposition 9 from Book 3 of Euclid's “Elements”)
If some point is taken inside a circle, and more than two equal straight lines radiate from the point towards the (circumference of the) circle, then the point taken is the center of the circle.
Modern Formulation
If a point $D$ can be connected with points on a circumference of a given circle such that more than two connecting segments have the same length, then $D$ must be the center of the circle.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1
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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