A cardboard circular disk of radius $5$ centimeters is placed on the table. While it is possible, Peter puts cardboard squares with side $5$ centimeters outside the disk so that: (1) one vertex of each square lies on the boundary of the disk; (2) the squares do not overlap; (3) each square has a common vertex with the preceding one. Find how many squares Peter can put on the table, and prove that the first and the last of them must also have a common vertex. (4 points)