Tinc un amic que li agrado.

Is this sentence translated correctly? I would think it means “I have a boyfriend that I love” since “agrado” is in the 1st person singular…

This phrase means: “I have a friend that likes me.”

This verbs works like this:

I like you = M’agrades (agrades is the conjugation for “you” secondpersonsingular).

I like Barcelona = M’agrada Barcelona (agrada is the 3rd person singular conjugation).

You have to ask who is being liked, not who is liking it.

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Let me add, as a native Catalan speaker, that this sentence has a totally equivalent one which removes the “who whom” confusion and is specific for expressing liking or infatuation with people:

“Tinc un amic que n’està, de mi!”
(I have a friend who likes me/ is infatuated with me)

As it happens with other genuine Catalan expressions, it is rarely heard in the more bilingualized areas of the country, but it is 100% correct and totally unambiguous. Maybe it could be offered as well as:

“Tinc un amic a qui li agrado” (notice the addition of the “a” to help clarify “who whom”)