Line AB = 10, Cd on line AB, if the length of AC is 1cm longer than 2 times of BC, then AC = cm

There may be some problems with the title. What's the use of D?
If point D is not considered and C is on the extension line of AB:
AC=AB+BC=2BC+1
Then BC = 9cm
AC=AB+BC=19cm
If C is on AB:
AC=AB-BC=2BC+1
Then BC = 3cm
AC=AB-BC=7cm

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