UKMT Pink Kangaroo, 2025

The figure shows a diameter of a smaller circle which lies along the diameter of a larger touching circle. It also shows a chord of the larger circle which is parallel to these diameters and is tangent to the smaller circle. The length of the chord is $16\text{ cm}$. What is the area of the shaded region?

(A) $16\pi\text{ cm}^2$ (B) $36\pi\text{ cm}^2$ (C) $49\pi\text{ cm}^2$ (D) $64\pi\text{ cm}^2$ (E) $81\pi\text{ cm}^2$