The word intricate was borrowed into English sometime in the early 1400s directly from Latin intricatus, which meant "entangled". While that differs slightly from the current definition of "complicated or detailed", one can clearly note the semantic connection. Intricatus is a conjugation of the verb intricare, which is composed of the prefix in-, meaning "in", and tricae, meaning "tricks" or "perplexities" (together, "in perplexities" describes entangled things pretty well). In- is the same as English in, and comes from the Proto-Indo-European root en, with the same meaning, and tricae is obscure. We know the word extricate ("out of perplexities") is a cognate, but not much else; the best guess is that it derives from PIE terk, which meant "to turn". Both intricate and extricate have been decreasing in usage in recent years.
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