What is the ratio of areas of circle inscribed and circumscribed in an equilateral triangle?

Problem: Given an equilateral triangle. What is the ratio of the area of a circle inscribed to the area of a circle circumscribed about the triangle?

Attempt: From what I understood, we have a circle inscribed in an equilateral triangle, and that triangle is inscribed to a circle. So we have two circles, big circle and small circle.

I am asked to find the ratio of the area of the small circle to the big circle. Let "s" be the area of the small circle and "b" for the big circle.

Ratio = Area of small circle / Area of big circle = $\frac{s}{b}$

The radius of the big circle is twice the radius of the small circle, so $R = 2r.$

Substituting the radius, Ratio = $\frac{\pi*r^2}{\pi*R^2}$ = $\frac{\pi*r^2}{\pi*(2r)^2}$ = $\frac{1}{4}$ = $1:4$

Question: Looking at the answer keys, the answer is supposed to be $\frac{1}{2}$ and not $\frac{1}{4}$. Any idea where did I got wrong or am I totally wrong? How to get the $\frac{1}{2}$. Thank you.