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Two Point Distance (Posted on 2010-06-25) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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re: Looking for the answer | Comment 3 of 4 |
(In reply to Looking for the answer by Dej Mar)

Hehe, I'm sure that you are right; as you can see, I had 3 goes at it!

I agree from my own research that the word 'sector' is not correct.  A sector is a pizza slice of a circle. The areas under the chords I suggested are segments; I did not find a special word for the odd shapes in the puzzle.

Over to you!

  Posted by broll on 2010-07-06 02:17:19
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