Among the options—Maine, Texas, Wyoming, Ohio—the correct answer is Wyoming. Its capital, Cheyenne, lies in the southeastern corner of the state but is nonetheless the capital closest to Wyoming's geographic center (which is near the town of Bates Hole, about 55 km / 34 miles north-northwest of Casper).
For comparison:
Note: Ohio's Columbus is very close to the state's geographic center; if multiple answers were allowed, Ohio would also qualify.