The Height of a Circular Arc Perpendicular to Chord line

Knowing the chord length and the centre height we need to find the Radius.

Multiplying out the brackets expands the equation to

Transposing for R gives

Theta is constant and can be found by

The constant height of the chord from the x axis simply

The equation of a circle is given by

Transposing for the y ordinate.

But the height to the curve less the chord height leaves the height from the chord to the arc.

Finally the total length of the arc is given by