Mathematica: Is there a clean method to find line segment intersections?

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Is there a clean method to find line segment intersections?
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(mathematica.stackexchange.com/users/82512/hana)hana
(mathematica.stackexchange.com/users/9362/bob-hanlon)Bob Hanlon
(mathematica.stackexchange.com/users/53172/azerbajdzan)azerbajdzan
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function-construction intersection functions