2025 Cayley Problem 15

In the diagram, \triangle ABC is right-angled at B and the semi-circle has diameter BC. If AB = 20 and AC = 40, what is the area of the semi-circle?

\textbf{(A)}\ 37.5\pi\quad \textbf{(B)}\ 75\pi\quad \textbf{(C)}\ 100\pi\quad \textbf{(D)}\ 150\pi\quad \textbf{(E)}\ 225\pi

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.