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Square in a Sector (Posted on 2007-06-06) Difficulty: 3 of 5
Let P and Q be points on a unit circle with center O such that angle POQ is x degrees ( x ≤ 270 ).
Let the bisector of angle POQ intersect the circle at point A.
Let KLMN be a square with vertices K and L on line segments OP and OQ and vertices M and N on the arc PAQ.

Give the area of the square in terms of x.

If x = 45, write the area of the square as (a+b√c)/d where a, b, c, and d are integers.

See The Solution Submitted by Bractals    
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Answer Comment 5 of 5 |
The required area of the square is (2 - V2)/3

  Posted by K Sengupta on 2009-01-09 15:39:32
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