I need help in finding a formula to calculate the radius (R) of a circle given the arc length (L) and the Chord Length (X)
Does anyone have any ideas how to solve this problem
Inconveniently. You can't solve for R directly, you first have to solve a transcendental equation for theta, the central angle of the arc. Working in radians
s = R*theta
c = 2*R*sin(theta/2)
Some manipulation leads to two equivalent forms in which R is eliminated
c/s = sin(theta/2) / (theta/2)
or sin(theta/2) - (c/s)*(theta/2) = 0
The first lets you set up a table for different theta of c/s and you can do reverse lookup and interpolation. The second can be used in Newton's method (along with the derivative) to rapidly converge on numerical value. Once you have theta/2, R = s/theta. Since Newton's method requires a decent starting guess, the table is still a good idea for the initial estimate (or a measurement off a drawing or something).
In theory, you could write theta = s/R and substitute in the chord equation. That does not lead to a general tabular method, and leaves a MUCH messier equation to solve by Newton's method, although it gives R directly.
Re: Radius calculation given Arc Length and Chord length
This is not possible......the reason for this is that the radius will vary with the angle subtended by the arc on the centre of the circle, i.e. as the angle subtended by the arc on the centre of the circle can have infinite number of values, the radius can also have infinite number of values.........hope this helps.....