Question

Question #1d57b

Answer 1

`sqrt2 : 1`

Explanation:

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`