The board of adjustment shall adopt rules to govern its procedure, in accordance with this chapter and any ordinance adopted under this chapter. The board shall designate, and may replace at any time, a chairman from among its members. Meetings of the board must be held at the call of the chairman and at any other time as the board may determine. Any two members of the board constitute a quorum. The chairman, or another member of the board designated by the chairman to serve as acting chairman, may administer oaths and compel the attendance of witnesses. All meetings of the board are open to the public. The board shall keep a full and accurate record of its proceedings, all documents filed with it, and all orders entered by the board. The record must be filed in the office of the board and is a public record.