2020 AMC 12B Problem 10

In unit square ABCD, the inscribed circle \omega intersects \overline{CD} at M, and \overline{AM} intersects \omega at a point P different from M. What is AP?

\textbf{(A) } \frac{\sqrt5}{12} \qquad \textbf{(B) } \frac{\sqrt5}{10} \qquad \textbf{(C) } \frac{\sqrt5}{9} \qquad \textbf{(D) } \frac{\sqrt5}{8} \qquad \textbf{(E) } \frac{2\sqrt5}{15}

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