In equal circles, angles standing upon equal circumferences are equal to one another, whether they are standing at the center or at the circumference.
Let two given circles be congruent and let some of its arcs be also congruent ($BC=EF$). Then the corresponding inscribed angles are also congruent ($\angle{BAC}=\angle{EDF}$) and the corresponding central angles are also congruent ($\angle{BGC}=\angle{EHF}$) are also congruent.
This is the converse of the Prop. 3.26.
Proofs: 1
Proofs: 1 2 3 4 5 6 7
Propositions: 8