2017 AMC 12B Problem 24

Quadrilateral ABCD has right angles at B and C, \triangle ABC \sim \triangle BCD, and AB > BC. There is a point E in the interior of ABCD such that \triangle ABC \sim \triangle CEB and the area of \triangle AED is 17 times the area of \triangle CEB. What is \frac{AB}{BC}?

\textbf{(A)}\ 1 + \sqrt{2} \qquad \textbf{(B)}\ 2 + \sqrt{2} \qquad \textbf{(C)}\ \sqrt{17} \qquad \textbf{(D)}\ 2 + \sqrt{5} \qquad\textbf{(E)}\ 1 + 2\sqrt{3}

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