There are three points A, B, and C which move around on the one circumference with a fixed speed, respectively.
A and B move to the same direction and C moves to the opposite direction of A and B.
These three points A, B, and C departed from the same point exactly at 1:00.
A and C met at 1:02 and B and C met for the first time after the start at 1:07.
Moreover, A returned to the original point for the first time at 1:02 30 seconds.
(1) Find the first time for B to return to the original point.
(2) Find the first time for A to catch up with B.
(3) Find the first time for A, B, and C to become three vertex of an equilateral triangle.