2024 AMC 12A Problem 19

Cyclic quadrilateral ABCD has lengths BC=CD=3 and DA=5 with \angle CDA=120^\circ. What is the length of the shorter diagonal of ABCD?

\textbf{(A) }\frac{31}7 \qquad \textbf{(B) }\frac{33}7 \qquad \textbf{(C) }5 \qquad \textbf{(D) }\frac{39}7 \qquad \textbf{(E) }\frac{41}7 \qquad

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