AHSME 1973 Problem 35

In the unit circle shown in the figure, chords $PQ$ and $MN$ are parallel to the unit radius $OR$ of the circle with center at $O$. Chords $MP$, $PQ$, and $NR$ are each $s$ units long and chord $MN$ is $d$ units long.

Of the three equations $$\textbf{I.}\ d-s=1, \textbf{II.}\ ds=1, \textbf{III.}\ d^2-s^2=\sqrt{5}$$ those which are necessarily true are $\textbf{(A)}\ \textbf{I}\ \text{only} \textbf{(B)}\ \textbf{II}\ \text{only} \textbf{(C)}\ \textbf{III}\ \text{only} \textbf{(D)}\ \textbf{I}\ \text{and}\ \textbf{II}\ \text{only} \textbf{(E)}\ \textbf{I, II}\ \text{and} \textbf{ III}$