Learn Arabic (Modern Standard): بفضل الدائرة، التصميم جميل. - Thanks to the circle, the design is beautiful.

It literally means "by the grace of" or "by the favor of," combining the prefix بـ (by/with) and the noun فضل (grace/favor). Because it acts as the first part of an Idafa (possessive construction), the following noun الدائرة takes the genitive case.

I usually see الدائرة translated as "department." Is that wrong here?

Not necessarily! While it translates to "circle" in a geometric or artistic context, الدائرة is also the standard word for a government or corporate "department" or "bureau." Depending on the broader context, this sentence could perfectly translate to "Thanks to the department, the design is beautiful."

Why is there no verb for "is" between التصميم and جميل?

This is a standard nominal sentence. In Arabic, equational sentences in the present tense do not use a "to be" verb. You simply place the definite subject التصميم (the design) right before the indefinite adjective جميل (beautiful) to create the complete thought "the design is beautiful."

Why is جميل indefinite when the subject التصميم is definite?

This difference in definiteness is exactly how Arabic shows that جميل is the predicate ("is beautiful") rather than just a descriptive adjective. If it were written as التصميم الجميل, it would mean "the beautiful design," which is just a noun phrase, not a complete sentence.