AMC 10A 2025 (Problem 10)

Plane GeometryMedium

A semicircle has diameter

\overline{AB}

and chord

\overline{CD}

of length

16

parallel to

\overline{AB}

. A smaller semicircle with diameter on

\overline{AB}

and tangent to

\overline{CD}

is cut from the larger semicircle, as shown below. What is the area of the resulting figure, shown shaded?

\text{(A)}\;16\pi

\text{(B)}\;24\pi

\text{(C)}\;32\pi

\text{(D)}\;48\pi

\text{(E)}\;64\pi