SOLUTION: A chord of a circle that is 16cm in length partitions another chord of the same circle into segments 6cm and 8cm. Find the lengths of the 16cm chord

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Question 742437: A chord of a circle that is 16cm in length partitions another chord of the same circle into segments 6cm and 8cm. Find the lengths of the 16cm chord
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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