Ratio of squares

A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the square's side and the circle's arc. What is the ratio of the areas of the large and small squares?

Correct answer:

r =  5111486:48007

Step-by-step explanation:

r1=1 u = 2 r1 = 2 a1  a1=2 r1/2=2 1/2=21.4142  r12 = a22 + (2 a2+a1/2)  r12=x2+(2 x+a1/2)  12=x2+(2 x+1.4142135623731/2) x22x+0.293=0 x2+2x0.293=0  a=1;b=2;c=0.293 D=b24ac=2241(0.293)=5.1715728753 D>0  x1,2=2ab±D=22±5.17 x1,2=1±1.137055 x1=0.137054624 x2=2.137054624 a2=x1=0.13710.1371  r2=2 a2/2=2 0.1371/20.0969  S1=a12=1.41422=2 S2=a22=0.137120.0188  r=S1/S2=2/0.0188106.4738=5111486:48007

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