Since this thread is obviously still live here are some useful formulae.

These are much better than the clumsy arcsin one from Wiki.

First Engineers used to use versed sine (versine) tables before calculators.

This easily gives the maximum rise from the chord if the radius and angle subtended to the centre are known.

A great many more offsets from the chord than just the centre one will be needed.

These can be calculated as in the first formula, after calculating the max offset.

An alternative are the offsets from the tangent (or any sideways displaced straight line) as shown in the second diagram.