There is one circle with radius $1$. There is another circle with radius $2$. They are tangent to each other and touch each other at point $c$. A line through $c$ splits the area formed by the two circles into two parts. The ratio of the two parts is $1:2$. In what ratio does the line split the area of the smaller circle (the circle with radius $1$)?
This was one of the questions in last year's AMC. I have no idea how to solve it. I thought that you could try and work out the of the two parts of the smaller circle and figure out what the ratio was between them. I tried that but failed. Thanks for any help.