The board of appeals shall have and exercise the following powers:

(A) To hear and decide appeals from any order, requirement, decision, or determination made by the administrative agency in the enforcement of the airport zoning regulations, as provided in sections 4563.11 and 4563.12 of the Revised Code.

(B) To hear and allow, refuse, or allow with modifications or conditions, any variance from the terms of the airport zoning regulations which the board may be authorized to pass upon pursuant to such regulations.

(C) To hear and decide specific variances under section 4563.16 of the Revised Code.