A circle reaching DC would reach neither the county seat nor the state capital. One reaching the state capital would also reach DC and Virginia. A circle extending from my home town in Tennessee to Memphis would reach a whopping buttload of states (close to 20).
Within 10 miles of my home address, I hit a number of cities (one major, the rest suburbs) 3 other counties. Also the State Capitol and Stone Mountain, but not Hartsfield-Jackson airport. Within 5 miles, also multiple cities, and 2 other counties.
I don’t really understand the circles, but I live 10 miles north of Anchorage, AK.
From here it’s 35 miles to the Virginia Beach oceanfront, 192 miles to Washington, D.C., 690 miles to my dad’s hometown in Florida, 710 miles to my old hometown of Indianapolis, 2,470 miles to my sister’s hometown in Nevada, and 5,190 miles away from the coldest city on Earth: Oymyakon, Russia.