In a circle, AB and CD are diameters. Which of the following must be true?

I. The length of arc ABD is equal to the length of arc BAC

II. AB is perpendicular to CD

III. ACBD is a square

Henry used 2/3 of the length of a board to make a box and 1/4 of the original length of the board to repair a step. The remaining piece of the board was 2 feet long. How many feet long was the original board?