Calculating the radius of a circular segment

[mklotz]

Hi:
I'm more geometry minded: The perpendicular bisectors of AP and BP would cross the center point, as well as the bisector of AB (PQ).
Carl.

Yes, your technique is exactly how the center-finder attachment on a combination square works.

However, if all you have is the circular segment, then that approach requires making an accurate drawing and constructing the perpendicular bisectors, and finally measuring the radius. All those manipulations are sources for added errror and, of course, take time.


With a segment, you make two measurements and the formula provides the desired value.

A good example of this is my technique for extending the range of calipers, explained here...

Extending the range of calipers

The process directly measures the chord and sagitta and the formula introduces no additional error. (A typical scientific calculator has 12 place accuracy).

BTW, you can't get more "geometry minded" than the intersecting chords theorem. It's one of the propositions in Euclid's Elements, a 2300 year old book that was the mainstay of geometry education for many centuries.