2024 AMC 8 Problem 18

Three concentric circles centered at O have radii of 1, 2, and 3. Points B and C lie on the largest circle. The region between the two smaller circles is shaded, as is the portion of the region between the two larger circles bounded by central angle BOC, as shown in the figure below. Suppose the shaded and unshaded regions are equal in area. What is the measure of \angle BOC in degrees?

\textbf{(A)} 108 \qquad \textbf{(B)} 120 \qquad \textbf{(C)} 135 \qquad \textbf{(D)} 144 \qquad \textbf{(E)} 150

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.