check this:
sin C = 4 / AC
or
sin C = 4 / 5 + x
also
sin C = 1 / x
4/5+x = 1/x
solve for x
x = 5/3
AC = 5 + 5/3
originally posted by jehantry this easier solution
complete the construction by drawing BD this is perpendicular to DC.radii meet tangents at 90 deg. triangle ABX is similar to BCD. each is a right triangle with angle ABX = to BCD. corresponding angles of parallellines thereforeAB /AX=BC/1 , AX=3,AB=5 BC =5/3, AC 15/3 +5/3= 20/3=6.666