The correct answer is C. The used verb form is correct.
The sentence “Bob is a friend of mine. I know him very well” is in the present tense. The verb “know” is a stative verb, which means that it describes a state of being rather than an action. Stative verbs are typically used in the present tense, even when they refer to something that happened in the past or will happen in the future. For example, you would say “I know Bob” even if you met him for the first time yesterday, and you would say “I will know Bob” even if you have not met him yet.
The options A, B, and D are all incorrect because they use the past participle form of the verb “know,” which is “known.” The past participle form of a verb is used to form perfect tenses and passive voice constructions. In this sentence, we are not talking about a perfect tense or a passive voice construction, so we need to use the present tense form of the verb, which is “know.”