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 2010-07-05 02:39:15