I wrote down the equations for the two circles and the line then intersected the line with the outer circle to get a relationship between the length of the line

I wrote down the equations for the two circles and the line then intersected the line with the outer circle to get a relationship between the length of the line and the two radii, calling this equation one. The second equation is the equation for the area of the annuli given their radii. Solving both equations for R^2-r^2 and equating gives the answer.