Semi-semicircle

Geometry Level 4

Take a semicircle of radius RR and one semicircle kk times bigger and make them tangent like in the picture above. Then construct a 90{{90}^{\circ }} arc through the midpoints of these 2 semicircles. If the shaded area is AA, calculate the ratio AkR2\dfrac{A}{kR^2}.

Hint: Notice that all three centers are collinear.

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