The 2 segments of each chord, when multiplied by each other need to equal each other.
In the image one chord is made up of 4 cm and 6 cm and the 2nd chord is made up of 3 cm and n
Setting p the equation to solve for n you have:
4 x 6 = 3 x n
Simplify:
24 = 3n
Divide both sides by 3:
n = 24/3
n = 8 cm