Answer:
∡BOA ≅ ∡DOC
Explanation:
Given a circle O with congruent chords BA and DC, you want the relation between angles BOA and DOC.
Congruence
All of the radii of circle O are congruent. That means BO≅AO≅DO≅CO. The chords BA and DC are marked as congruent. This means ∆BOA and ∆DOC are congruent by the SSS postulate.
Corresponding parts of congruent triangles are congruent, so ...
∡BOA ≅ ∡DOC