In the figure, $\mathrm{R}$ is the midpoint of $\stackrel{-}{\mathrm{P}\mathrm{Q}}.$ What is the measure of $\mathrm{\angle }\mathrm{O}\mathrm{R}\mathrm{Q}$?

In the figure, $\mathrm{A}\mathrm{B}$ and $\mathrm{C}\mathrm{D}$ are two equal chords of a circle with center $\mathrm{O}$. $\mathrm{OP}$ and $\mathrm{O}\mathrm{Q}$ are perpendiculars to chords $\mathrm{A}\mathrm{B}$ and $\mathrm{C}\mathrm{D}$ respectively. If $\mathrm{\angle }\mathrm{P}\mathrm{O}\mathrm{Q}={150}^{\mathrm{o}},$ then what is $\mathrm{\angle }\mathrm{A}\mathrm{P}\mathrm{Q}?$

In the figure, $\mathrm{O}\mathrm{A}=5\mathrm{}\mathrm{c}\mathrm{m},\mathrm{}\mathrm{}\mathrm{A}\mathrm{B}=8\mathrm{}\mathrm{c}\mathrm{m}\mathrm{}$ and $\mathrm{O}\mathrm{D}$ is perpendicular to $\mathrm{A}\mathrm{B},$ then what is the length of $\mathrm{C}\mathrm{D}?$