In the given figure, a circle O is inscribed in a square ABCD of area S. The tangency points of the circle with the sides of the square are labeled E, F, G, and H.
Point M is the intersection of lines DF and AG, and point N is the intersection of line DF and circle O.
Let S_{1} denote the area of triangle GMN. Prove that S equals 40 times S_{1}.
Square holds circle tight,
Triangle forms at their meet.
Area, what's the plight?
See also:
Typography of problem 371. |