Problem 371: Square, Inscribed circle, Triangle, Area

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The figure shows a circle 1 inscribed in a square ABCD of area S. Points E, F, G, and H are the tangency point. M is the point of intersection of DF and AG and N is de point of intersection of DF and circle 1. If S1 is the area of triangle GMN, prove that S = 40S1. .

Square, triangle, inscribed circle, area

  

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