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c = 10.5

Step-by-step explanation:

Formula: the product of the lengths of the segments of one chord equal the product of the segments of the other.

              a •d = c • b

               7*12 = c*8

                 84 =8c

Divide by 8

                 84/8 = 8c/8

                 10.5 = c

step-by-step explanation:

given that ab is divided into equal parts as

ac, cd, de, ef, fg, gh, hi, ib.

from this we find that f is the midpoint of ab.

so using mid point formula we find

f = (3,7)

similarly considering fb, we get

h = mid point of fb = ((6,6) and g, mid point of fh is

g = (9/2, 13/2)

i is mid point of hb

so i =(15/2,11/2)