1. Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line passing through F and H. Consider points P and Q, on L and inside ABCD such that the angles APD and BQC both equal 120°. What is the ratio of the area of ABQCDP to the remaining area inside ABCD?
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By: anil on 05 May 2019 02.29 am
Consider side of square as 10 units. So HD=5 and HP=$$frac{5}{sqrt3}$$ . So now area of triangle HPD=$$frac{12.5}{sqrt3}$$. Also Area APD=Area BQC=2*AreaHPD=$$frac{25}{sqrt3}$$. So numerator of required answer is $$100-frac{50}{sqrt3}$$ and denominator as $$frac{50}{sqrt3}$$. Solving we get answer as $$2sqrt{3}-1$$.
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