The answer is A. The detective searched the area following the robbery. The definite article "the" is one of the most important words used frequently in English. It is normally used in front of a noun. In this case, the noun is the word Detective. A definite article can be used in various circumstances, e.g. in front of adjectives or collective nouns just to name a few. Therefore, the definite article is used when someone knows what he/she is referring to.
It was the "Magna Carta" that first granted the right of citizens to ask the king for help, and this was a major inspiration for western countries in terms of "checking" the power of kinds and queens.