2019 AMC 10B Problem 16

In \triangle ABC with a right angle at C, point D lies in the interior of \overline{AB} and point E lies in the interior of \overline{BC} so that AC=CD, DE=EB, and the ratio AC:DE=4:3. What is the ratio AD:DB?

\textbf{(A) } 2:3 \qquad\textbf{(B) } 2:\sqrt{5} \qquad\textbf{(C) } 1:1 \qquad\textbf{(D) } 3:\sqrt{5} \qquad\textbf{(E) } 3:2

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