I know that the following can be answered easily using trigonometric ratios, but is there any way to go about it without relying on trigonometry? (The book from which the problem was taken doesn't cover trig before this point.)
$O$ is the centre of a circle, and $PQ$ and $RS$ are two equal length chords in it. Points $M$ and $N$ are the midpoints of the two chords $PQ$ and $RS$ respectively. The length of $PQ$ is given as $6$cm and the measure of the angle $\angle POQ$ (where $O$ is the vertex) is given as $80^\circ$ degrees. A diagram of this is in the snapshot I've attached. The question is, how do you calculate the length $|OM|$?