Three points moving on three circles

As shown in a figure, there are three circles centering on the point O and radii are 1m, 2m, and 3m, respectively.

Point A on the most inside circumference, point B on the next circumference, point C on the most outside circumference are moving clockwise, respectively.

The ratio of the speed of A : B : C is 1 : 3 : 2.

Three points start from the position where O, A, B, and C are on a straight line at this order and point A goes one round in 12 seconds. Answer the following questions.

(1) What round is each point moved round by the time when three points A, B, and C return to the position of the start simultaneously for the first time?

(2) During the time of (1), how many times does the angle made by OA and OB become right-angled?

(3) Consider in 10 minutes after starting.

(3)-1 How many times does the angle made by OA and OB become right-angled?

(3)-2 How many times does the angle made by OA and OC become right-angled?

Answer