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Quantitative Ability and Data Interpretation Question on Geometry

Consider a square ABCD with midpoints E, F, G and H of sides AB, BC, CD and DA. Let L denote the line passing through F and H. Consider points P and Q on the line L inside the square such that the angles APD and BQC are both equal 120 degrees. What is the ratio ABQCDP to the remaining area of ABCD?

A

423\frac {4\sqrt 2}{3}

B

23−12\sqrt 3-1

C

2+32+\sqrt 3

D

10−339\frac {10-3\sqrt 3}{9}

Answer

23−12\sqrt 3-1

Explanation

Solution

The correct option is (B): 23−12\sqrt 3-1.