contingo

Contingo, contingere, contigi, contactum is third conjugation, cum plus tango with the vowel weakened, so the perfect drops the nasal: contigi, not contingi. English contact comes straight off the supine.

The two senses are one idea seen from either end. Something that touches you happens to you, and from that the verb becomes impersonal: contingit ut with the subjunctive, "it comes about that". Classical usage adds a flavour English loses, since contingit tends to mark good luck while accidit leans towards the unwelcome and evenit is neutral. In practice later writers ignore the distinction. Watch the two present forms: contingit is present, contigit is perfect, and one letter is the whole difference.