Midrash for Ketubot 90:8
דבר אחר שעריך ולא שערי עובדי כוכבים האי שעריך הא אפיקתיה אם כן לימא קרא שער מאי שעריך שמע מינה תרתי
Another interpretation: “Your gates” but not the gates of non-Jews. But this phrase “Your gates” have you not already deduced something from it? If so, the verse should have said “gate”; why “Your gates”? You can learn from it two things.
Sifrei Devarim
"in one of your cities": What is the intent of this? Because it is written (Ibid. 5) "Then you shall take out that man or that woman who did this evil thing, to your cities (lit., "gates"), I might think, the reference is to the gate (i.e., the beth-din) in which he was judged; it is, therefore, written "gates" (verse 2), "gates" (verse 5). Just as "gates" (2) refers to the city in which they were found and not to the gate (beth-din) in which they were judged, so, "gates" (5) refers to the city in which they were found and not to the gate (beth-din) in which they were judged.
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