AMC 12 2023b Problem 3

A $3-4-5$ right triangle is inscribed in circle $A$, and a $5-12-13$ right triangle is inscribed in circle $B$. What is the ratio of the area of circle $A$ to the area of circle $B$?

\textbf{(A)}\frac{9}{25} \textbf{(B)}\frac{1}{9} \textbf{(C)}\frac{1}{5} \textbf{(D)}\frac{25}{169} \textbf{(E)}~\frac{4}{25}