If you know the radius that you want and the distance between the outside points on the arc, here is how you calculate the middle point location.
C = radius
L = length between end points on the arc
Run a line from the center point of the circle through a point that bisects L, That line will intersect the third point on the arc.
To simplify the math, use A as 1/2 L, C as the radius and B as the line from the center to the cord line.
A² + B
² = C ²
B² = C² - A²
B = The distance from the line to the arc is C - B
Example:
Radius = 20
Length between points = 6
From center point of circle to line is:
20² - 6² = 400 - 36 = 364
B =
= 19.078
Distance from center point of line to arc is 20 - 19.078 = .922 Ft = 11.064 inches