Question #1d57b

1 Answer
CW
Apr 7, 2017

sqrt2 : 1

Explanation:

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Let r_1 be the radius of the smaller circle and r_2 be the radius of the larger circle, as shown in the figure.

By Pythagorean theorem, we know that
r_2^2=r_1^2+r_1^2
=> r_2^2=2r_1^2
=> r_2=sqrt2r_1

circumference of smaller circle C_1=2pir_1
circumference of larger circle C_2=2pir_2=2sqrt2pir_1

Hence, C_2 : C_1 = 2sqrt2pir_1 : 2pir_1=sqrt2 : 1

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