If radius b is double that of radius a, the area of the smaller circle to that of the larger circle is in proportion :
b = 2a
area of circle = $$\pi r^2$$
 The area of the smaller circle to that of the larger circle is in proportion = $$\pi a^2 : \pi b^2 =  a^2 : 4a^2 = 1 : 4$$
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