Step 1: Given $$OA \times OB = OC \times OD \Rightarrow \frac{OA}{OC} = \frac{OD}{OB}$$
Step 2: In $\triangle OAD$ and $\triangle OCB$, $\angle AOD = \angle COB$ (vertically opposite angles).
Step 3: By SAS similarity criterion,
$$\triangle OAD \sim \triangle OCB$$
Step 4: Corresponding angles of similar triangles are equal, therefore
$$\angle OAD = \angle OCB \Rightarrow \angle A = \angle C$$

Correct option : (A)