Learn Croatian: Na audiciju je došao takav akrobat kakvog publika nikada nije vidjela. - The kind of acrobat the audience has never seen came to the audition.

They form a correlative pair used to describe a specific quality, meaning "the kind of... that" or "such a... as". Here, takav introduces the acrobat in the main clause, and kakvog links to the relative clause that explains exactly what kind of acrobat he is.

Why do we use takav in the first part but kakvog in the second part? Shouldn't they be in the same case?

They agree in gender (masculine) and number (singular), but their cases depend on their grammatical roles in their own clauses. Takav is nominative because the acrobat is the subject of the main clause. Kakvog is accusative because it represents the direct object of the verb vidjela (the audience saw him). Because akrobat is a living being, the masculine accusative takes the genitive form (kakvog).

Why is the verb vidjela in the feminine form if the acrobat is a man?

In the relative clause, the subject doing the seeing is publika (the audience). Because publika is a grammatically feminine noun in Croatian, the past participle must be feminine (vidjela) to agree with it.

Just a quick refresher: why do we say nikada nije?