If the arc length (l) between the extreme points defining the chord are known, and the conditions given and the radius of the circle (R), the problem of computing the length of the chord (m) can be reduced to the calculation of the base length of an isosceles triangle. The sides of this triangle are formed by two radii of a circle, and the angle between them will be the Central angle you need to calculate in the first place. To do this, divide the length of the arc of the radius l/R. the result is expressed in radians. If you prefer to calculate in degrees, the formula would be much more difficult - first, multiply the length of the arc by 360, and then divide the result by twice the product of PI times the radius: l*360/(2*π*R) = l*180/(π*R).
After ascertaining the size of the Central angle, calculate the length of the chord. This doubled the radius of the circle, multiply by the sine of half the Central angle. If you have chosen calculations in degrees, in General, the obtained formula, write down: m = 2*R*sin(l*90/(π*R)). For the calculations in radians and it will contain one less mathematical operation m = 2*R*sin(l/(2*R)). For example, if the arc length of 90 cm and radius 60 cm chord must have a length of 2*60*sin(90*90/(3,14*60)) = 120*sin(8100/188,4) = 120*sin(42,99°) ≈ 120*0,68 = 81,6 cm with the accuracy of the calculations to two decimal places.
If, in addition to the arc length (l) in terms of the problem given full circumference (L) Express through it the radius, divided by twice the number PI. Then substitute this expression into the General formula from the previous step: m = 2*(L/(2*π))*sin(l*90/(π*L/(2*π))). After simplification of the expression you should have this equality for the calculations in the degree m = L/π*sin(l*180/L). For calculations in radians it will look like this: m = L/π*sin(l*π/L). For example, if the arc length is 90 cm and the length of a circle 376,8 cm, length of the chord will be 376,8/3,14*sin(90*180/376,8) = 120*sin(42,99°) ≈ 120*0,68 = 81,6 see