A circle has a radius of 1 unit with its center located at O and P is an arbitrary point inside the circle. Three straight lines are drawn from P to meet the circle’s circumference respectively at the points A, B and C.
It is known that:
Angle APB = Angle BPC = Angle APC = 120 degrees, and:
Area of sector APB = pi/3 square units, and:
Area of sector BPC = pi/4 square units.
Determine the length of the straight line OP.
I am really interested in trying to solve this problem, yet I am having some difficulty. I know broll has tried to formulate a solution, yet I know it is not quite correct or complete.
One of the problems I am having is the use of the term sector. By definintion, neither APB nor BPC are sectors. It may help to find a calcuable solution (without resorting to calculus to which I would not wish to do) if there was a correct term I might research for possible equations that relate.
Can you provide the correct terminology?

Posted by Dej Mar
on 20100705 02:39:15 