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If I am not wrong, no matter how many dots you have in that circle, it will have infinite lines. All circles have infinite straight lines.
If you are talking about other lines and not straight lines, then my answer is not applicable.
Assuming you mean to ask, "How many times can I connect ten dots on the outer edge of a circle?", then the answer is 42. If you're not connecting dots immediately next to each other, then you can draw only 32 lines.
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