Two points moving on a diameter

The figure is a circle centering on the point O with radius of 6 cm.

The diameters AB and CD cross right-angled.

The point P leaves A and goes back and forth between A and O at 3 cm/s without stopping.

The point Q leaves B and goes back and forth between B and O at 2 cm/s without stopping.

P and Q leave at the same time.

(1) Find the area of the triangle CPQ 5 seconds after P and Q leave. Moreover, find the numbers of seconds after leaving when it becomes the same area at next time.

(2) Find the area of the triangle CPQ 116 seconds after P and Q leave.

(3) There is a time when the area of the portion excluding the triangle CPQ from the circle is to be 107.04 cm².

Find the number of seconds after P and Q leave when it becomes this area at 6th times.

Pi is assumed to be 3.14.

Answer