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Circumscribing puzzle



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Red area = Rectangle - 2 triangles.

Inner circle has r=1 (area = pi*r^2=pi). Inner square has length 2, hence diagonally sqrt(2) is the radius of the outer circle, hence the outer square has length 2*sqrt(2).

Rectangle has area (1+sqrt(2))*sqrt(2) = 2 + sqrt(2)

Leftlower triangle has area (sqrt(2))^2/2= 2/2 = 1.

Uppermost triangle has area (sqrt(2)-1)*1/2

Therefore the area of the red triangle is 2+sqrt(2)-1-sqrt(2)/2+1/2=(3+sqrt(2)/2.

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