In unit square A B C D, the inscribed circle \omega intersects \overline{C D} at M, and \overline{A M} intersects \omega at a point P different from M. What is A P ?
Answer Choices
A. \dfrac{\sqrt{5}}{12}
B. \dfrac{\sqrt{5}}{10}
C. \dfrac{\sqrt{5}}{9}
D. \dfrac{\sqrt{5}}{8}
E. \dfrac{2 \sqrt{5}}{15}