If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal.

In the figure $\mathrm{A}\mathrm{B}$ is a diameter of the circle $\mathrm{C}\mathrm{D}$ is a chord equal to radius of the circle. $\mathrm{A}\mathrm{C}\mathrm{}$and $\mathrm{B}\mathrm{D}$ when produced meet at $\mathrm{E}$. Prove that $\mathrm{\angle }\mathrm{A}\mathrm{E}\mathrm{B}=60°$.

In the figure, $\mathrm{ABCD}$ is a cyclic quadrilateral such that $\mathrm{AC} \mathrm{and} \mathrm{BD}$ are its diagonals. If $\angle \mathrm{DBC}=55° \mathrm{and} \angle \mathrm{BAC}=45°$ and $\angle \mathrm{BCD}=k°$, then find $k$.

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