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7.
The first line can separate the circle into at most 2 sectors, because the line is straight and only has 1 sector to divide. The second line can separate the circle into at most 4 sectors because it is a straight line and only has 2 sectors to divide. When drawing the third line, there are 4 sectors which could be divided, but because the line is straight it can only reach 3 of the sectors, thus dividing 3 of the original 4 sectors into 6 sectors and leaving one of the original 4 sectors untouched, which totals 7 sectors.
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