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.
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
(1) 21 cm2
7 seconds
(2) 24 cm2
(3) 34 seconds
7 seconds
(2) 24 cm2
(3) 34 seconds
