Learn Hardcore Russian: Причина моей радости — помощь друга. - The reason for my joy is help from a friend.

In Russian, when the verb “to be” (есть) is omitted in the present tense, a dash (тире) often links the subject and its complement. Here Причина моей радости is the subject and помощь друга is the predicate noun, so the dash shows that “help from a friend” defines or identifies the “reason for my joy.”

Why is моей in the genitive case? Could we use the nominative instead?

Моей is the feminine singular genitive form of мой, because it modifies радости, which itself is in the genitive case. In Russian, the noun причина (“reason”) takes a genitive-dependent phrase to indicate “the reason of something,” so you say причина чего? (the reason of what?) – моей радости (“of my joy”).

Why does радости end with -и?

Радость is a feminine noun ending in a soft sign (ь). Such nouns form their genitive singular by replacing the soft sign with -и, giving радости.

What case is помощь in, and why?

Помощь is in the nominative case, acting as the predicate noun after the dash. In sentences where a noun names or defines the subject (with an omitted “to be”), the complement noun remains in the nominative.

Why is друга in the genitive rather than the instrumental?

When you use помощь as a noun (“help”), Russian typically takes the provider of that help in the genitive: помощь кого? (“help of whom?”) – друга. The instrumental case (другом) would appear with the verb помогать (“to help someone”), not with the noun помощь.

Can I rephrase this with a clause instead of a noun phrase?

Yes. You could say:
Причина моей радости в том, что друг помог мне.
Here в том, что introduces a subordinate clause (“that a friend helped me”) to explain the reason.