1963 AHSME Problem 10

Point P is taken interior to a square with side-length a and such that is it equally distant from two consecutive vertices and from the side opposite these vertices. If d represents the common distance, then d equals:

\textbf{(A)}\ \frac{3a}{5}\qquad \textbf{(B)}\ \frac{5a}{8}\qquad \textbf{(C)}\ \frac{3a}{8}\qquad \textbf{(D)}\ \frac{a\sqrt{2}}{2}\qquad \textbf{(E)}\ \frac{a}{2}

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