Proposition: 3.26: Equal Angles and Arcs in Equal Circles
(Proposition 26 from Book 3 of Euclid's “Elements”)
In equal circles, equal angles stand upon equal circumferences whether they are standing at the center or at the circumference.
![fig26e](https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/euclid/Book03/fig26e.png?raw=true)
Modern Formulation
Let two given circles be congruent and let some of its inscribed angles be congruent ($\angle{BAC}=\angle{EDF}$) or some of its central angles be congruent ($\angle{BGC}=\angle{EHF}$) be congruent. Then the corresponding arcs are also congruent ($BKC=ELF$).
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4 5
Propositions: 6
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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