I must admit that I find a certain satisfaction in the geometry that pops up in general carpentry. Fine Homebuilding has a nice video on drawing a circular arch that uses a basic geometric construction. This is something that I expect to be doing soon so I thought I would document it here. The interesting part to me is the basic geometry. Basically, the construction uses a tape measure as a compass. I will just add the following figure, which shows the basic approach.
This discussion focused on using geometric methods to determine the radius. You can use algebra to determine the radius. The following figure illustrates how to go about the derivation and provides an algebraic result.