Question

How to find the length of chord if the length of the arc is given

Answer 1

The length a of the arc is a fraction of the length of the circumference which is 2 π r. In fact the fraction is a/2πr

The angle t is a fraction of the central angle of the circle which is 360 degrees. It's the same fraction. Thus

t = 360 ×  a/2πr
degrees.

S is the midpoint of RQ so |SQ| = c/2 and the measure of the angle SPQ is 
t/2.
Also QSP is a right angle so
sin(t/2)= |SQ|/r.
Hence
|SQ| = r × sin(t/2)
and thus

c = 2 × r × sin(t/2).

Answer 2

I hope my answer is right