We know that central angles are congruent, because it is given. We can say that segments AO, CO, BO, and DO are congruent because . Then by the congruency theorem, we know that triangle AOC is congruent to triangle BOD. Finally, we can conclude that chord AC is congruent to chord BD because .

The central angles that intercept chords AC and BD are ∠AOC and ∠BOD, so choice A gives the angle pair used in the proof. The segments AO, CO, BO, and DO are radii of the same circle and are therefore congruent. With the included central angles congruent, the triangles are congruent by SAS; then AC ≅ BD by corresponding parts of congruent triangles.

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