With the same configuration and $D$ the midpoint of arc $BDC$, which of the following are correct? (i) $\angle BDC = \angle BAC$, (ii) $\angle BAC = \frac{1}{2}\angle BOC$ is FALSE here (since $\angle BOC$ is reflex), (iii) $\angle BOC = \angle DBC + \angle BCD$. The correct combination is—

Statement (i) holds because $\angle BDC$ and $\angle BAC$ stand on the same arc $BC$ and are angles in the same segment, so they are equal. Statement (iii) is the exterior-angle (or triangle angle-sum applied to $\triangle BDC$ relating to the central angle) relation that holds here, while (ii) fails because is reflex; hence the correct combination is i and iii.