<PRE><B>Question 742437</B>
Let x = length of first piece of the 16 cm chord


So 16-x is the remaining second piece of the same 16 cm chord


By the intersecting chords theorem, we can say


6*8 = x*(16-x)


48 = 16x - x^2


0 = -x^2 + 16x - 48


-x^2 + 16x - 48 = 0


x^2 - 16x + 48 = 0


(x - 12)(x - 4) = 0


x-12 = 0 or x-4 = 0


x = 12 or x = 4


So the 16 cm chord breaks up into two pieces which are 12 cm and 4 cm</PRE>